Hodge classes and the Jacquet-Langlands correspondence

Atsushi Ichino; Kartik Prasanna

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arXiv · 1806.10563

Hodge classes and the Jacquet-Langlands correspondence

Atsushi Ichino·Kartik Prasanna

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Abstract

We prove that the Jacquet-Langlands correspondence for cohomological automorphic forms on quaternionic Shimura varieties is realized by a Hodge class. Conditional on Kottwitz's conjecture for Shimura varieties attached to unitary similitude groups, we also show that the image of this Hodge class in $\ell$-adic cohomology is Galois invariant for all $\ell$.

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Atsushi Ichino, Kartik Prasanna. 2018-06-27. Hodge classes and the Jacquet-Langlands correspondence. https://arxiv.org/abs/1806.10563

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