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Publications of Kirsten G. Wickelgren    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds363234,
   Author = {Arcila-Maya, N and Bethea, C and Opie, M and Wickelgren, K and Zakharevich, I},
   Title = {Compactly supported A1-Euler characteristic and
             the Hochschild complex},
   Journal = {Topology and Its Applications},
   Volume = {316},
   Year = {2022},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.topol.2022.108108},
   Abstract = {We show the A1-Euler characteristic of a smooth, projective
             scheme over a characteristic 0 field is represented by its
             Hochschild complex together with a canonical bilinear form,
             and give an exposition of the compactly supported A1-Euler
             characteristic [Formula presented] from the Grothendieck
             group of varieties to the Grothendieck–Witt group of
             bilinear forms. We also provide example computations.},
   Doi = {10.1016/j.topol.2022.108108},
   Key = {fds363234}
}

@article{fds361735,
   Author = {Kuhn, N and Mallory, D and Thatte, V and Wickelgren,
             K},
   Title = {An explicit self-duality},
   Year = {2021},
   Month = {November},
   Abstract = {We provide an exposition of the canonical self-duality
             associated to a presentation of a finite, flat, complete
             intersection over a Noetherian ring, following work of
             Scheja and Storch.},
   Key = {fds361735}
}

@article{fds355950,
   Author = {Pauli, S and Wickelgren, K},
   Title = {Applications to A1 -enumerative geometry of the
             A1 -degree},
   Journal = {Research in Mathematical Sciences},
   Volume = {8},
   Number = {2},
   Year = {2021},
   Month = {June},
   url = {http://dx.doi.org/10.1007/s40687-021-00255-6},
   Abstract = {These are lecture notes from the conference Arithmetic
             Topology at the Pacific Institute of Mathematical Sciences
             on applications of Morel’s A1-degree to questions in
             enumerative geometry. Additionally, we give a new dynamic
             interpretation of the A1-Milnor number inspired by the
             first-named author’s enrichment of dynamic intersection
             numbers.},
   Doi = {10.1007/s40687-021-00255-6},
   Key = {fds355950}
}

@article{fds355951,
   Author = {Srinivasan, P and Wickelgren, K},
   Title = {An arithmetic count of the lines meeting four lines in
             P3},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {374},
   Number = {5},
   Pages = {3427-3451},
   Year = {2021},
   Month = {May},
   url = {http://dx.doi.org/10.1090/tran/8307},
   Abstract = {We enrich the classical count that there are two complex
             lines meeting four lines in space to an equality of
             isomorphism classes of bilinear forms. For any field k, this
             enrichment counts the number of lines meeting four lines
             defined over k in P3k, with such lines weighted by their
             fields of definition together with information about the
             cross-ratio of the intersection points and spanning planes.
             We generalize this example to an infinite family of such
             enrichments, obtained using an Euler number in A1-homotopy
             theory. The classical counts are recovered by taking the
             rank of the bilinear forms.},
   Doi = {10.1090/tran/8307},
   Key = {fds355951}
}

@article{fds358017,
   Author = {Bachmann, T and Wickelgren, K},
   Title = {EULER CLASSES: SIX-FUNCTORS FORMALISM, DUALITIES,
             INTEGRALITY and LINEAR SUBSPACES of COMPLETE
             INTERSECTIONS},
   Journal = {Journal of the Institute of Mathematics of
             Jussieu},
   Year = {2021},
   Month = {January},
   url = {http://dx.doi.org/10.1017/S147474802100027X},
   Abstract = {We equate various Euler classes of algebraic vector bundles,
             including those of [12] and one suggested by M. J. Hopkins,
             A. Raksit, and J.-P. Serre. We establish integrality results
             for this Euler class and give formulas for local indices at
             isolated zeros, both in terms of the six-functors formalism
             of coherent sheaves and as an explicit recipe in the
             commutative algebra of Scheja and Storch. As an application,
             we compute the Euler classes enriched in bilinear forms
             associated to arithmetic counts of d-planes on complete
             intersections in <! > in terms of topological Euler numbers
             over < > and <! >.},
   Doi = {10.1017/S147474802100027X},
   Key = {fds358017}
}

@article{fds355952,
   Author = {Leo Kass and J and Wickelgren, K},
   Title = {An arithmetic count of the lines on a smooth cubic
             surface},
   Journal = {Compositio Mathematica},
   Pages = {677-709},
   Year = {2021},
   Month = {January},
   url = {http://dx.doi.org/10.1112/S0010437X20007691},
   Abstract = {We give an arithmetic count of the lines on a smooth cubic
             surface over an arbitrary field, generalizing the counts
             that over there are lines, and over the number of hyperbolic
             lines minus the number of elliptic lines is. In general, the
             lines are defined over a field extension and have an
             associated arithmetic type in. There is an equality in the
             Grothendieck-Witt group of, where denotes the trace. Taking
             the rank and signature recovers the results over and. To do
             this, we develop an elementary theory of the Euler number
             in-homotopy theory for algebraic vector bundles. We expect
             that further arithmetic counts generalizing enumerative
             results in complex and real algebraic geometry can be
             obtained with similar methods.},
   Doi = {10.1112/S0010437X20007691},
   Key = {fds355952}
}

@article{fds348838,
   Author = {Kass, JL and Wickelgren, K},
   Title = {A classical proof that the algebraic homotopy class of a
             rational function is the residue pairing},
   Journal = {Linear Algebra and Its Applications},
   Volume = {595},
   Pages = {157-181},
   Year = {2020},
   Month = {June},
   url = {http://dx.doi.org/10.1016/j.laa.2019.12.041},
   Abstract = {© 2020 Elsevier Inc. Cazanave has identified the algebraic
             homotopy class of a rational function of 1 variable with an
             explicit nondegenerate symmetric bilinear form. Here we show
             that Hurwitz's proof of a classical result about real
             rational functions essentially gives an alternative proof of
             the stable part of Cazanave's result. We also explain how
             this result can be interpreted in terms of the residue
             pairing and that this interpretation relates the result to
             the signature theorem of Eisenbud, Khimshiashvili, and
             Levine, showing that Cazanave's result answers a question
             posed by Eisenbud for polynomial functions in 1 variable.
             Finally, we announce results answering this question for
             functions in an arbitrary number of variables.},
   Doi = {10.1016/j.laa.2019.12.041},
   Key = {fds348838}
}

@article{fds361507,
   Author = {Arcila-Maya, N and Bethea, C and Opie, M and Wickelgren, K and Zakharevich, I},
   Title = {Compactly supported $\mathbb{A}^{1}$-Euler characteristic
             and the Hochschild complex},
   Year = {2020},
   Month = {March},
   Abstract = {We show the $\mathbb{A}^{1}$-Euler characteristic of a
             smooth, projective scheme over a characteristic $0$ field is
             represented by its Hochschild complex together with a
             canonical bilinear form, and give an exposition of the
             compactly supported $\mathbb{A}^{1}$-Euler characteristic
             $\chi^{c}_{\mathbb{A}^{1}}: K_0(\mathbf{Var}_{k}) \to
             \text{GW}(k)$ from the Grothendieck group of varieties to
             the Grothendieck--Witt group of bilinear forms. We also
             provide example computations.},
   Key = {fds361507}
}

@article{fds352550,
   Author = {Bethea, C and Kass, JL and Wickelgren, K},
   Title = {Examples of wild ramification in an enriched
             riemann–hurwitz formula},
   Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
             Later},
   Volume = {745},
   Pages = {69-82},
   Year = {2020},
   Month = {January},
   url = {http://dx.doi.org/10.1090/conm/745/15022},
   Abstract = {© 2020 American Mathematical Society. M. Levine proved an
             enrichment of the classical Riemann–Hurwitz formula to an
             equality in the Grothendieck–Witt group of quadratic
             forms. In its strongest form, Levine’s theorem includes a
             technical hypothesis on ramification relevant in positive
             characteristic. We describe what happens when the hypotheses
             are weakened by showing an analogous Riemann–Hurwitz
             formula and describing an example suggested by S.
             Saito.},
   Doi = {10.1090/conm/745/15022},
   Key = {fds352550}
}

@article{fds345574,
   Author = {Kass, JL and Wickelgren, K},
   Title = {The class of Eisenbud-Khimshiashvili-Levine is the local A
             1 -Brouwer degree},
   Journal = {Duke Mathematical Journal},
   Volume = {168},
   Number = {3},
   Pages = {429-469},
   Year = {2019},
   Month = {February},
   url = {http://dx.doi.org/10.1215/00127094-2018-0046},
   Abstract = {Given a polynomial function with an isolated zero at the
             origin, we prove that the local A1-Brouwer degree equals the
             Eisenbud-Khimshiashvili-Levine class. This answers a
             question posed by David Eisenbud in 1978. We give an
             application to counting nodes, together with associated
             arithmetic information, by enriching Milnor's equality
             between the local degree of the gradient and the number of
             nodes into which a hypersurface singularity bifurcates to an
             equality in the Grothendieck-Witt group.},
   Doi = {10.1215/00127094-2018-0046},
   Key = {fds345574}
}

@article{fds345575,
   Author = {Bergner, JE and Joachimi, R and Lesh, K and Stojanoska, V and Wickelgren, K},
   Title = {Classification of problematic subgroups of
             U(n)},
   Journal = {Transactions of the American Mathematical
             Society},
   Volume = {371},
   Number = {10},
   Pages = {6739-6777},
   Year = {2019},
   Month = {January},
   url = {http://dx.doi.org/10.1090/tran/7442},
   Abstract = {Let Ln denote the topological poset of decompositions of
             ℂn into mutually orthogonal subspaces. We classify p-toral
             subgroups of U(n) that can have noncontractible fixed points
             under the action of U(n) on Ln.},
   Doi = {10.1090/tran/7442},
   Key = {fds345575}
}

@article{fds345576,
   Author = {Wickelgren, K and Williams, B},
   Title = {The simplicial EHP sequence in A1–algebraic
             topology},
   Journal = {Geometry & Topology},
   Volume = {23},
   Number = {4},
   Pages = {1691-1777},
   Year = {2019},
   Month = {January},
   url = {http://dx.doi.org/10.2140/gt.2019.23.1691},
   Abstract = {© 2019, Mathematical Sciences Publishers. All rights
             reserved. We give a tool for understanding simplicial
             desuspension in A1–algebraic topology: We show that
             X→Ω(S1∧ X) → Ω(S1∧ X∧ X) is a fiber sequence up
             to homotopy in 2–localized A1 algebraic topology for X =
             (S1)m∧ G∧qm with m > 1. It follows that there is an EHP
             spectral sequence (Formula Presented.)},
   Doi = {10.2140/gt.2019.23.1691},
   Key = {fds345576}
}

@article{fds348483,
   Author = {Wickelgren, K and Williams, B},
   Title = {Unstable Motivic Homotopy Theory},
   Booktitle = {Handbook of Homotopy Theory},
   Publisher = {CRC Press},
   Year = {2019},
   ISBN = {0815369700},
   Abstract = {The Handbook of Homotopy Theory provides a panoramic view of
             an active area in mathematics that is currently seeing
             dramatic solutions to long-standing open problems, and is
             proving itself of increasing importance across many other
             ...},
   Key = {fds348483}
}

@article{fds361653,
   Author = {Davis, R and Pries, R and Wickelgren, K},
   Title = {The Galois action on the lower central series of the
             fundamental group of the Fermat curve},
   Year = {2018},
   Month = {August},
   Abstract = {Information about the absolute Galois group $G_K$ of a
             number field $K$ is encoded in how it acts on the \'etale
             fundamental group $\pi$ of a curve $X$ defined over $K$. In
             the case that $K=\mathbb{Q}(\zeta_n)$ is the cyclotomic
             field and $X$ is the Fermat curve of degree $n \geq 3$,
             Anderson determined the action of $G_K$ on the \'etale
             homology with coefficients in $\mathbb{Z}/n \mathbb{Z}$.The
             \'etale homology is the first quotient in the lower central
             series of the \'etale fundamental group.In this paper, we
             determine the structure of the graded Lie algebra for $\pi$.
             As a consequence, this determines the action of $G_K$ on all
             degrees of the associated graded quotient of the lower
             central series of the \'etale fundamental group of the
             Fermat curve of degree $n$, with coefficients in
             $\mathbb{Z}/n \mathbb{Z}$.},
   Key = {fds361653}
}

@article{fds345577,
   Author = {Davis, R and Pries, R and Stojanoska, V and Wickelgren,
             K},
   Title = {The Galois action and cohomology of a relative homology
             group of Fermat curves},
   Journal = {Journal of Algebra},
   Volume = {505},
   Pages = {33-69},
   Year = {2018},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.jalgebra.2018.02.021},
   Abstract = {For an odd prime p satisfying Vandiver's conjecture, we give
             explicit formulae for the action of the absolute Galois
             group GQ(ζp) on the homology of the degree p Fermat curve,
             building on work of Anderson. Further, we study the
             invariants and the first Galois cohomology group which are
             associated with obstructions to rational points on the
             Fermat curve.},
   Doi = {10.1016/j.jalgebra.2018.02.021},
   Key = {fds345577}
}

@article{fds345578,
   Author = {Kass, JL and Wickelgren, K},
   Title = {An Étale realization which does NOT exist},
   Volume = {707},
   Pages = {11-29},
   Booktitle = {Contemporary Mathematics},
   Year = {2018},
   Month = {January},
   url = {http://dx.doi.org/10.1090/conm/707/14251},
   Abstract = {For a global field, local field, or finite field k with
             infinite Galois group, we show that there cannot exist a
             functor from the Morel-Voevodsky A1-homotopy category of
             schemes over k to a genuine Galois equivariant homotopy
             category satisfying a list of hypotheses one might expect
             from a genuine equivariant category and an étale
             realization functor. For example, these hypotheses are
             satisfied by genuine ℤ/2-spaces and the R-realization
             functor constructed by Morel-Voevodsky. This result does not
             contradict the existence of étale realization functors to
             (pro-)spaces, (pro-)spectra or complexes of modules with
             actions of the absolute Galois group when the endomorphisms
             of the unit is not enriched in a certain sense. It does
             restrict enrichments to representation rings of Galois
             groups.},
   Doi = {10.1090/conm/707/14251},
   Key = {fds345578}
}

@article{fds345579,
   Author = {Wickelgren, K},
   Title = {Massey products 〈y,x,x,…,x,x,y〉 in Galois cohomology
             via rational points},
   Journal = {Journal of Pure and Applied Algebra},
   Volume = {221},
   Number = {7},
   Pages = {1845-1866},
   Year = {2017},
   Month = {July},
   url = {http://dx.doi.org/10.1016/j.jpaa.2016.12.027},
   Abstract = {For x an element of a field other than 0 or 1, we compute
             the order n Massey products 〈(1−x)−1,x−1,…,x−1,(1−x)−1〉
             of n−2 factors of x−1 and two factors of (1−x)−1 by
             embedding P1−{0,1,∞} into its Picard variety and
             constructing Gal(ks/k) equivariant maps from π1et applied
             to this embedding to unipotent matrix groups. This method
             produces obstructions to π1-sections of P1−{0,1,∞},
             partial computations of obstructions of Jordan Ellenberg,
             and also computes the Massey products 〈x−1,(−x)−1,…,(−x)−1,x−1〉.},
   Doi = {10.1016/j.jpaa.2016.12.027},
   Key = {fds345579}
}

@article{fds345580,
   Author = {Asok, A and Wickelgren, K and Williams, B},
   Title = {The simplicial suspension sequence in A1-homotopy},
   Journal = {Geometry & Topology},
   Volume = {21},
   Number = {4},
   Pages = {2093-2160},
   Year = {2017},
   Month = {May},
   url = {http://dx.doi.org/10.2140/gt.2017.21.2093},
   Abstract = {We study a version of the James model for the loop space of
             a suspension in unstable A1-homotopy theory. We use this
             model to establish an analog of G W Whitehead’s classical
             refinement of the Freudenthal suspension theorem in
             A1-homotopy theory: our result refines F Morel’s
             A1-simplicial suspension theorem. We then describe some
             E1-differentials in the EHP sequence in A1-homotopy theory.
             These results are analogous to classical results of G W
             Whitehead. Using these tools, we deduce some new results
             about unstable A1-homotopy sheaves of motivic spheres,
             including the counterpart of a classical rational
             nonvanishing result.},
   Doi = {10.2140/gt.2017.21.2093},
   Key = {fds345580}
}

@article{fds345581,
   Author = {Wickelgren, K},
   Title = {Desuspensions of S 1 Λ (P1/Q - {0, 1, ∞
             })},
   Journal = {International Journal of Mathematics},
   Volume = {27},
   Number = {7},
   Year = {2016},
   Month = {June},
   url = {http://dx.doi.org/10.1142/S0129167X16400103},
   Abstract = {We use the Galois action on Q1 -{0, 1,∞}) to show that the
             homotopy equivalence S1 Λ (Gm, Gm, S1 (1 -{0, 1,∞})
             coming from purity, does not desuspend to a map Gm, Gm, 1
             -{0, 1,∞}.},
   Doi = {10.1142/S0129167X16400103},
   Key = {fds345581}
}

@article{fds345582,
   Author = {Wickelgren, K},
   Title = {What is… an anabelian scheme?},
   Journal = {Notices of the American Mathematical Society},
   Volume = {63},
   Number = {3},
   Pages = {285-286},
   Year = {2016},
   Month = {March},
   url = {http://dx.doi.org/10.1090/noti1342},
   Doi = {10.1090/noti1342},
   Key = {fds345582}
}

@article{fds346310,
   Author = {Davis, R and Pries, R and Stojanoska, V and Wickelgren,
             K},
   Title = {Galois Action on the Homology of Fermat Curves},
   Volume = {3},
   Pages = {57-86},
   Year = {2016},
   Month = {January},
   url = {http://dx.doi.org/10.1007/978-3-319-30976-7_3},
   Abstract = {In his paper titled “Torsion points on Fermat
             Jacobians, roots of circular units and relative singular
             homology,” Anderson determines the homology of the
             degree n Fermat curve as a Galois module for the action of
             the absolute Galois group (Forumala presented). In
             particular, when n is an odd prime p, he shows that the
             action of (Forumala presented). on a more powerful relative
             homology group factors through the Galois group of the
             splitting field of the polynomial (Forumala presented). If p
             satisfies Vandiver’s conjecture, we give a proof that
             the Galois group G of this splitting field over (Forumala
             presented). is an elementary abelian p-group of rank
             (Forumala presented). Using an explicit basis for G, we
             completely compute the relative homology, the homology, and
             the homology of an open subset of the degree 3 Fermat curve
             as Galois modules. We then compute several Galois cohomology
             groups which arise in connection with obstructions to
             rational points. In Anderson (Duke Math J 54(2):501 –
             561, 1987), the author determines the homology of the degree
             n Fermat curve as a Galois module for the action of the
             absolute Galois group (Forumala presented). In particular,
             when n is an odd prime p, he shows that the action of
             (Forumala presented). on a more powerful relative homology
             group factors through the Galois group of the splitting
             field of the polynomial (Forumala presented). If p satisfies
             Vandiver’s conjecture, we give a proof that the
             Galois group G of this splitting field over (Forumala
             presented). is an elementary abelian p-group of rank
             (Forumala presented). Using an explicit basis for G, we
             completely compute the relative homology, the homology, and
             the homology of an open subset of the degree 3 Fermat curve
             as Galois modules. We then compute several Galois cohomology
             groups which arise in connection with obstructions to
             rational points.},
   Doi = {10.1007/978-3-319-30976-7_3},
   Key = {fds346310}
}

@article{fds348345,
   Title = {Women in Topology},
   Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
             Later},
   Publisher = {American Mathematical Society},
   Year = {2015},
   Month = {May},
   url = {http://dx.doi.org/10.1090/conm/641},
   Doi = {10.1090/conm/641},
   Key = {fds348345}
}

@article{fds345584,
   Author = {Hopkins, MJ and Wickelgren, KG},
   Title = {Splitting varieties for triple Massey products},
   Journal = {Journal of Pure and Applied Algebra},
   Volume = {219},
   Number = {5},
   Pages = {1304-1319},
   Year = {2015},
   Month = {May},
   url = {http://dx.doi.org/10.1016/j.jpaa.2014.06.006},
   Abstract = {We construct splitting varieties for triple Massey products.
             For a, b, c∈F* the triple Massey product 〈a, b, c〉 of
             the corresponding elements of H1(F, μ2) contains 0 if and
             only if there are x∈F* and y∈F[a,c]* such that
             bx2=NF[a,c]/F(y), where NF[a,c]/F denotes the norm, and F is
             a field of characteristic different from 2. These varieties
             satisfy the Hasse principle by a result of D.B. Leep and
             A.R. Wadsworth. This shows that triple Massey products for
             global fields of characteristic different from 2 always
             contain 0.},
   Doi = {10.1016/j.jpaa.2014.06.006},
   Key = {fds345584}
}

@article{fds345583,
   Author = {Kass, JL and Wickelgren, K},
   Title = {An Abel map to the compactified Picard scheme realizes
             Poincaré duality},
   Journal = {Algebraic & Geometric Topology},
   Volume = {15},
   Number = {1},
   Pages = {319-369},
   Year = {2015},
   Month = {March},
   url = {http://dx.doi.org/10.2140/agt.2015.15.319},
   Abstract = {For a smooth algebraic curve X over a field, applying H1 to
             the Abel map X→PicX∕∂X to the Picard scheme of X
             modulo its boundary realizes the Poincaré duality
             isomorphism H1(X,Z∕ℓ)→H1(X∕∂X,Z∕ℓ(1))≅H1c(X,Z∕ℓ(1)).
             We show the analogous statement for the Abel map
             X/∂X→Pic X/∂X to the compactified Picard, or Jacobian,
             scheme, namely this map realizes the Poincaré duality
             isomorphism H1(X∕∂X,Z∕ℓ)→H1(X,Z∕ℓ(1)). In
             particular, H1 of this Abel map is an isomorphism. In
             proving this result, we prove some results about Pic that
             are of independent interest. The singular curve X∕∂X has
             a unique singularity that is an ordinary fold point, and we
             describe the compactified Picard scheme of such a curve up
             to universal homeomorphism using a presentation scheme. We
             construct a Mayer–Vietoris sequence for certain pushouts
             of schemes, and an isomorphism of functors
             πℓ1Pic0(−)≅H1(−,Zℓ(1)).},
   Doi = {10.2140/agt.2015.15.319},
   Key = {fds345583}
}

@article{fds345585,
   Author = {Wickelgren, K},
   Title = {2-Nilpotent real section conjecture},
   Journal = {Mathematische Annalen},
   Volume = {358},
   Number = {1-2},
   Pages = {361-387},
   Year = {2014},
   Month = {February},
   url = {http://dx.doi.org/10.1007/s00208-013-0967-5},
   Abstract = {We show a 2-nilpotent section conjecture over ℝ: for a
             geometrically connected curve X over ℝ such that each
             irreducible component of its normalization has ℝ-points,
             π0(X(ℝ)) is determined by the maximal 2-nilpotent
             quotient of the fundamental group with its Galois action, as
             the kernel of an obstruction of Jordan Ellenberg. This
             implies that for X smooth and proper, X(ℝ)± is determined
             by themaximal 2-nilpotent quotient of Gal(ℂ(X)) with its
             Gal(ℝ) action, where X(ℝ)± denotes the set of real
             points equipped with a real tangent direction, showing a
             2-nilpotent birational real section conjecture. © 2013
             Springer-Verlag Berlin Heidelberg.},
   Doi = {10.1007/s00208-013-0967-5},
   Key = {fds345585}
}

@article{fds348346,
   Author = {Wickelgren, K},
   Title = {Cartier’s first theorem for Witt vectors on
             ℤ_{≥0}ⁿ-0},
   Journal = {Surveys on Discrete and Computational Geometry: Twenty Years
             Later},
   Pages = {321-328},
   Publisher = {American Mathematical Society},
   Year = {2014},
   ISBN = {9780821894743},
   url = {http://dx.doi.org/10.1090/conm/620/12396},
   Doi = {10.1090/conm/620/12396},
   Key = {fds348346}
}

@article{fds348347,
   Author = {Wickelgren, K},
   Title = {n-nilpotent obstructions to pi(1)sections of P-1 - {0, 1,
             infinity} and Massey products},
   Journal = {Galois Teichmueller Theory and Arithmetic
             Geometry},
   Volume = {63},
   Pages = {579-600},
   Publisher = {MATH SOC JAPAN},
   Editor = {Nakamura, H and Pop, F and Schneps, L and Tamagawa,
             A},
   Year = {2012},
   Month = {January},
   ISBN = {978-4-86497-014-3},
   Key = {fds348347}
}

@article{fds345586,
   Author = {Wickelgren, K},
   Title = {On 3-nilpotent obstructions to π1 sections for
             ℙ1-{0,1,∞}},
   Pages = {281-328},
   Booktitle = {The Arithmetic of Fundamental Groups: PIA
             2010},
   Year = {2012},
   Month = {January},
   ISBN = {9783642239045},
   url = {http://dx.doi.org/10.1007/978-3-642-23905-2_12},
   Abstract = {We study which rational points of the Jacobian of
             ℙ1-{0,1,∞} can be lifted to sections of geometrically
             3-nilpotent quotients of étale π1 over the absolute Galois
             group. This is equivalent to evaluating certain triple
             Massey products of elements of k* ⊆ H1(Gk, ℤ(1)) or
             H1(Gk,ℤ/2ℤ). For k = ℚp or R, we give a complete mod 2
             calculation. This permits some mod 2 calculations for k =
             ℚ. These are computations of obstructions of Jordan
             Ellenberg.},
   Doi = {10.1007/978-3-642-23905-2_12},
   Key = {fds345586}
}

@article{fds353836,
   Author = {Wickelgren, K},
   Title = {3-nilpotent obstructions to pi_1 sections for P^1_Q -
             {0,1,infty}},
   Journal = {The Arithmetic of Fundamental Groups Pia 2010, Editor J.
             Stix, Contributions in Mathematical and Computational
             Sciences, Vol. 2, Springer Verlag Berlin Heidelberg,
             2012},
   Editor = {Stix, J},
   Year = {2012},
   Month = {January},
   Abstract = {We study which rational points of the Jacobian of P^1_K
             -{0,1,infty} can be lifted to sections of geometrically 3
             nilpotent quotients of etale pi_1 over the absolute Galois
             group. This is equivalent to evaluating certain triple
             Massey products of elements of H^1(G_K). For K=Q_p or R, we
             give a complete mod 2 calculation. This permits some mod 2
             calculations for K = Q. These are computations of
             obstructions of Jordan Ellenberg.},
   Key = {fds353836}
}

@article{fds345587,
   Author = {Vakil, R and Wickelgren, K},
   Title = {Universal covering spaces and fundamental groups in
             algebraic geometry as schemes},
   Journal = {Journal De Theorie Des Nombres De Bordeaux},
   Volume = {23},
   Number = {2},
   Pages = {489-526},
   Year = {2011},
   Month = {January},
   url = {http://dx.doi.org/10.5802/jtnb.774},
   Abstract = {In topology, the notions of the fundamental group and the
             universal cover are closely intertwined. By importing usual
             notions from topology into the algebraic and arithmetic
             setting, we construct a fundamental group family from a
             universal cover, both of which are schemes. A geometric
             fiber of the fundamental group family (as a topological
             group) is canonically the étale fundamental group. The
             constructions apply to all connected quasicompact
             quasiseparated schemes. With different methods and
             hypotheses, this fundamental group family was already
             constructed by Deligne. © Société Arithmétique de
             Bordeaux.},
   Doi = {10.5802/jtnb.774},
   Key = {fds345587}
}

@article{fds345588,
   Author = {Iams, S and Katz, B and Silva, CE and Street, B and Wickelgren,
             K},
   Title = {On weakly mixing and doubly ergodic nonsingular
             actions},
   Journal = {Colloquium Mathematicum},
   Volume = {103},
   Number = {2},
   Pages = {247-264},
   Year = {2005},
   Month = {January},
   url = {http://dx.doi.org/10.4064/cm103-2-10},
   Abstract = {We study weak mixing and double ergodicity for nonsingular
             actions of locally compact Polish abelian groups. We show
             that if T is a nonsingular action of G, then T is weakly
             mixing if and only if for all cocompact subgroups A of G the
             action of T restricted to A is weakly mixing. We show that a
             doubly ergodic nonsingular action is weakly mixing and
             construct an infinite measure-preserving flow that is weakly
             mixing but not doubly ergodic. We also construct an infinite
             measure-preserving flow whose cartesian square is
             ergodic.},
   Doi = {10.4064/cm103-2-10},
   Key = {fds345588}
}

 

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