Date: Monday, November 14, 2016
Location: 4088 East Hall (4:10 PM to 5:30 PM)
Title: Hodge classes and the JacquetLanglands 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 JacquetLanglands 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.
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Speaker: Kartik Prasanna
Institution: University of Michigan
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