Algebraic cycles and tate classes on hilbert modular varieties

Journal Article

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 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.

Full Text

Duke Authors

Cited Authors

  • Getz, JR; Hahn, H

Published Date

  • February 1, 2014

Published In

Volume / Issue

  • 10 / 1

Start / End Page

  • 161 - 176

International Standard Serial Number (ISSN)

  • 1793-0421

Digital Object Identifier (DOI)

  • 10.1142/S1793042113500875

Citation Source

  • Scopus