Seminar Event Detail

Group, Lie and Number Theory

Date:  Monday, November 14, 2016
Location:  4088 East Hall (4:10 PM to 5:30 PM)

Title:  Hodge classes and the Jacquet-Langlands correspondence

Abstract:   I will discuss the relation between Langlands functoriality and the theory of algebraic cycles in one of the simplest instances of functoriality, namely the Jacquet-Langlands correspondence for Hilbert modular forms. In this case, functoriality gives rise to a family of Tate classes on products of quaternionic Shimura varieties. The Tate conjecture predicts that these classes come from an algebraic cycle, which in turn should give rise to a compatible Hodge class. While we cannot yet prove the Tate conjecture in this context, I will outline an unconditional proof of the existence of such a Hodge class and discuss some applications. This is joint work (in progress) with A. Ichino.


Speaker:  Kartik Prasanna
Institution:  University of Michigan

Event Organizer:     


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