Periods of quaternionic Shimura varieties

Periods of quaternionic Shimura varieties

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Kartik Prasanna, University of Michigan, Ann Arbor
IAS Room S-101

In the early 80's, Shimura made a precise conjecture relating Peterssoninner products of arithmetic automorphicforms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture (which is a consequence of the Tate conjecture on algebraic cycles) was proved a few years later by Michael Harris. In the first half of my talk I will motivate and describe an integral version of Shimura's conjecture i.e. up to p-adic units for a good prime p. In the second half I will describe work in progress (joint with Atsushi Ichino) that makes some progress in understanding this refined conjecture.