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- W2116920605 abstract "Let $E/mathbb{Q}$ be a totally real number field that is Galois over $mathbb{Q}$, and let $pi$ be a cuspidal, nondihedral automorphic representation of $mathrm{GL}_2(mathbb{A}_E)$ that is in the lowest weight discrete series at every real place of $E$. The representation $pi$ cuts out a $M_mathrm{et}(pi^{infty})$ from the $ell$-adic middle degree intersection cohomology of an appropriate Hilbert modular variety. If $ell$ is sufficiently large in a sense that depends on $pi$ we compute the dimension of the space of Tate classes in $M_mathrm{et}(pi^{infty})$. 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 $M_mathrm{et}(pi^{infty})$ is spanned by algebraic cycles." @default.
- W2116920605 created "2016-06-24" @default.
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- W2116920605 date "2015-07-16" @default.
- W2116920605 modified "2023-09-27" @default.
- W2116920605 title "Algebraic cycles and Tate classes on Hilbert modular varieties" @default.
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