Periods of Quaternionic Shimura Varieties. I.
About this Title
Atsushi Ichino, Kyoto University, Kyoto, Japan and Kartik Prasanna, University of Michigan, Ann Arbor, MI
Publication: Contemporary Mathematics
Publication Year: 2021; Volume 762
ISBNs: 978-1-4704-4894-3 (print); 978-1-4704-6418-9 (online)
This book formulates a new conjecture about quadratic periods of automorphic forms on quaternion algebras, which is an integral refinement of Shimura's algebraicity conjectures on these periods. It also provides a strategy to attack this conjecture by reformulating it in terms of integrality properties of the theta correspondence for quaternionic unitary groups. The methods and constructions of the book are expected to have applications to other problems related to periods, such as the Bloch-Beilinson conjecture about special values of $L$-functions and constructing geometric realizations of Langlands functoriality for automorphic forms on quaternion algebras.
Graduate students and research mathematicians interested in number theory, automorphic forms, Shimura varieties, and $L$-functions.
Table of Contents
- Atsushi Ichino and Kartik Prasanna – Periods of Quaternionic Shimura Varieties. I.