Periods of quaternionic Shimura varieties. I
Number Theory
2016-10-04 v1
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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Cite
@article{arxiv.1610.00166,
title = {Periods of quaternionic Shimura varieties. I},
author = {Atsushi Ichino and Kartik Prasanna},
journal= {arXiv preprint arXiv:1610.00166},
year = {2016}
}
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173 pages