Publications [#292892] of Jayce R. Getz

Papers Published

1. Getz, JR; Hahn, H, Algebraic cycles and tate classes on hilbert modular varieties, International Journal of Number Theory, vol. 10 no. 1 (February, 2014), pp. 161-176, ISSN 1793-0421 [doi]
   (last updated on 2024/04/16)

   Abstract:
   Let E/ be a totally real number field that is Galois over , and let be a cuspidal, nondihedral automorphic representation of GL2(E) that is in the lowest weight discrete series at every real place of E. The representation cuts out a motive Mét(π∞) from the ℓ-adic 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.