%% Papers Published
@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}
}
@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{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
ℙ1ℚ-{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{fds348346,
Author = {Wickelgren, K},
Title = {Cartier’s first theorem for Witt vectors on
ℤ_{≥0}ⁿ-0},
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{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{fds345583,
Author = {Kass, JL and Wickelgren, K},
Title = {An Abel map to the compactified Picard scheme realizes
Poincaré duality},
Journal = {Algebraic and 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{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{fds348345,
Title = {Women in Topology},
Publisher = {American Mathematical Society},
Editor = {Basterra, M and Bauer, K and Hess, K and Johnson,
B},
Year = {2015},
Month = {May},
url = {http://dx.doi.org/10.1090/conm/641},
Doi = {10.1090/conm/641},
Key = {fds348345}
}
@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{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{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{fds345580,
Author = {Asok, A and Wickelgren, K and Williams, B},
Title = {The simplicial suspension sequence in A1-homotopy},
Journal = {Geometry and 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{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{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{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{fds348483,
Author = {Wickelgren, K and Williams, B},
Title = {Unstable Motivic Homotopy Theory},
Booktitle = {Handbook of Homotopy Theory},
Publisher = {CRC Press},
Year = {2019},
ISBN = {9780815369707},
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{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 and 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{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{fds352550,
Author = {Bethea, C and Kass, JL and Wickelgren, K},
Title = {Examples of wild ramification in an enriched
riemann–hurwitz formula},
Journal = {Contemporary Mathematics},
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{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{fds355952,
Author = {Leo Kass and J and Wickelgren, K},
Title = {An arithmetic count of the lines on a smooth cubic
surface},
Journal = {Compositio Mathematica},
Volume = {157},
Number = {4},
Pages = {677-709},
Year = {2021},
Month = {April},
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 k, generalizing the counts
that over C there are 27 lines, and over R the number of
hyperbolic lines minus the number of elliptic lines is 3. In
general, the lines are defined over a field extension L and
have an associated arithmetic type α in L∗/(L∗)2. There
is an equality in the Grothendieck–Witt group GW(k) of k,
∑ TrL/k <α> = 15 · <1> + 12 · <−1>, lines where TrL/k
denotes the trace GW(L) → GW(k). Taking the rank and
signature recovers the results over C and R. To do this, we
develop an elementary theory of the Euler number in
A1-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{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{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{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{fds368292,
Author = {Kuhn, N and Mallory, D and Thatte, V and Wickelgren,
K},
Title = {An explicit self-duality},
Volume = {480},
Booktitle = {Stacks Project Expository Collection (SPEC)},
Publisher = {Cambridge University Press},
Editor = {Belmans, P and Ho, W and de Jong, AJ},
Year = {2022},
Month = {October},
ISBN = {9781009054850},
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 = {fds368292}
}
@article{fds374300,
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},
Journal = {Israel Journal of Mathematics},
Year = {2023},
Month = {January},
url = {http://dx.doi.org/10.1007/s11856-023-2571-z},
Abstract = {Information about the absolute Galois group GK of a number
field K is encoded in how it acts on the étale fundamental
group π of a curve X defined over K. In the case that K =
ℚ(ζn) is the cyclotomic field and X is the Fermat curve
of degree n ≥ 3, Anderson determined the action of GK on
the étale homology with coefficients in ℤ/nℤ. The
étale homology is the first quotient in the lower central
series of the étale fundamental group. In this paper, we
determine the Galois module structure of the graded Lie
algebra for π. As a consequence, this determines the action
of GK on all degrees of the associated graded quotient of
the lower central series of the étale fundamental group of
the Fermat curve of degree n, with coefficients in
ℤ/nℤ.},
Doi = {10.1007/s11856-023-2571-z},
Key = {fds374300}
}
@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},
Volume = {22},
Number = {2},
Pages = {681-746},
Year = {2023},
Month = {March},
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{fds372441,
Author = {Bachmann, T and Wickelgren, K},
Title = {On quadratically enriched excess and residual
intersections},
Journal = {Journal fur die Reine und Angewandte Mathematik},
Volume = {2023},
Number = {802},
Pages = {77-123},
Year = {2023},
Month = {September},
url = {http://dx.doi.org/10.1515/crelle-2023-0041},
Abstract = {We use recent duality results of Eisenbud and Ulrich to give
tools to study quadratically enriched residual intersections
when there is no excess bundle. We use this to prove a
formula for the Witt-valued Euler number of an almost
complete intersection. We give example computations of
quadratically enriched excess and residual
intersections.},
Doi = {10.1515/crelle-2023-0041},
Key = {fds372441}
}
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Mathematics Department