Yifeng Liu : Height paring of special divisors on unitary Shimura curves

Posted by Ramin Takloo-Bighash , part of the Number Theory Seminar.

At

Dec. 4, 2012, 4 p.m.

In

SEO 636

Abstract

In this talk, I will introduce a class of divisors on Shimura curves associated to certain unitary groups, which consist of the unitary version of the Heegner points. The idea comes from the theta lifting, a key construction in the theory of automorphic representations. We show that the height of those divisors is related to the central L-derivative of automorphic forms of unitary groups of 2 variables. In fact, these construction and relation can be generalized to unitary groups of higher ranks, which correspond to higher dimensional Shimura varieties, as well. A precise formulation of the height formula will be given.

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