Periods of quaternionic Shimura varieties

by Prof. Kartik Prasanna (University of Michigan, Ann Arbor, USA)

Thursday, August 18, 2011 from 14:30 to 15:30 (Asia/Kolkata)
at Colaba Campus ( AG-77 )

Description

In the early 80's, Shimura made a precise conjecture (up to algebraic
factors) relating Petersson inner products of arithmetic automorphic forms
on quaternion algebras over a totally real field. This conjecture (which is
a consequence of the Tate conjecture on algebraic cycles) was mostly 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.