Math @ Duke

Publications [#292892] of Jayce R. Getz
Papers Published
 Getz, JR; Hahn, H, Algebraic cycles and tate classes on hilbert modular varieties,
International Journal of Number Theory, vol. 10 no. 1
(2014),
pp. 161176, ISSN 17930421 [doi]
(last updated on 2017/12/16)
Abstract: Let E/ be a totally real number field that is Galois over , and let be a cuspidal, nondihedral automorphic representation of GL 2 ( E ) that is in the lowest weight discrete series at every real place of E. The representation cuts out a motive M ét (π ∞ ) from the ℓadic middle degree intersection cohomology of an appropriate Hilbert modular variety. If ℓ is sufficiently large in a sense that depends on π we compute the dimension of the space of Tate classes in M ét (π ∞ ). Moreover if the space of Tate classes on this motive over all finite abelian extensions k/E is at most of rank one as a Hecke module, we prove that the space of Tate classes in M ét (π ∞ ) is spanned by algebraic cycles. © 2014 World Scientific Publishing Company.


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