Periods of quaternionic Shimura varieties. I

2016/10/01 by Atsushi Ichino, Ichino, Atsushi, Kartik Prasanna +1 · 1 citation
Mathematics · #11F27 #11F41 #11G18 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.00166

openalex publication_date 2016/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study "quadratic periods" on quaternionic Shimura varieties and formulate an integral refinement of Shimura's conjecture regarding Petersson inner products of automorphic forms that are related by the Jacquet-Langlands correspondence. The main result is that this integral refinement is implied by another conjecture (Conjecture D below) regarding integrality of theta lifts between certain quaternionic unitary groups.

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