Hodge classes and the Jacquet-Langlands correspondence

Atsushi Ichino; Kartik Prasanna

Hodge classes and the Jacquet-Langlands correspondence

Number Theory 2023-07-12 v2

Authors: Atsushi Ichino , Kartik Prasanna

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 $\ell$ .

Keywords

hodge class jacquet-langlands correspondence automorphic forms shimura varieties galois invariance

Cite

@article{arxiv.1806.10563,
  title  = {Hodge classes and the Jacquet-Langlands correspondence},
  author = {Atsushi Ichino and Kartik Prasanna},
  journal= {arXiv preprint arXiv:1806.10563},
  year   = {2023}
}

Comments

118 pages. Revised version following referee reports. Changes to introduction, Sec. 9 and Sec. 11, minor edits elsewhere. To be published in Forum of Math, Pi

Hodge classes and the Jacquet-Langlands correspondence

Abstract

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