School of Mathematics Seminars and Lectures
Periods of quaternionic Shimura varieties
by Prof. Kartik Prasanna (University of Michigan, Ann Arbor, USA)
Thursday, August 18, 2011
from
to
(Asia/Kolkata)
at Colaba Campus ( AG-77 )
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. |