Skip to main content
Journal cover image

Algebraic cycles and tate classes on hilbert modular varieties

Publication ,  Journal Article
Getz, JR; Hahn, H
Published in: International Journal of Number Theory
February 1, 2014

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.

Duke Scholars

Published In

International Journal of Number Theory

DOI

ISSN

1793-0421

Publication Date

February 1, 2014

Volume

10

Issue

1

Start / End Page

161 / 176

Related Subject Headings

  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Getz, J. R., & Hahn, H. (2014). Algebraic cycles and tate classes on hilbert modular varieties. International Journal of Number Theory, 10(1), 161–176. https://doi.org/10.1142/S1793042113500875
Getz, J. R., and H. Hahn. “Algebraic cycles and tate classes on hilbert modular varieties.” International Journal of Number Theory 10, no. 1 (February 1, 2014): 161–76. https://doi.org/10.1142/S1793042113500875.
Getz JR, Hahn H. Algebraic cycles and tate classes on hilbert modular varieties. International Journal of Number Theory. 2014 Feb 1;10(1):161–76.
Getz, J. R., and H. Hahn. “Algebraic cycles and tate classes on hilbert modular varieties.” International Journal of Number Theory, vol. 10, no. 1, Feb. 2014, pp. 161–76. Scopus, doi:10.1142/S1793042113500875.
Getz JR, Hahn H. Algebraic cycles and tate classes on hilbert modular varieties. International Journal of Number Theory. 2014 Feb 1;10(1):161–176.
Journal cover image

Published In

International Journal of Number Theory

DOI

ISSN

1793-0421

Publication Date

February 1, 2014

Volume

10

Issue

1

Start / End Page

161 / 176

Related Subject Headings

  • 0101 Pure Mathematics