Math @ Duke
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Publications [#223281] of Jayce R. Getz
Papers Published
- J.R. Getz and H. Hahn, Algebraic cycles and Tate classes on Hilbert modular varieties,
Int. J. Number Theory, vol. 10 no. 1
(2014),
pp. 161-176
(last updated on 2014/04/17)
Abstract: Let E be a totally real number field that is Galois, and consider a cuspidal, nondihedral automorphic representation of GL(2) over E that is in the lowest weight discrete series at every real place of E. The representation cuts out a ``motive'' M 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 the representation we compute the dimension of the space of Tate classes in M. 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 is spanned by algebraic cycles.
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