|Date: Tuesday, January 04, 2022
Location: Virtual (4:00 PM to 5:00 PM)
Title: Eichler-Shimura relations
Abstract: The well-known classical Eichler-Shimura relation for modular curves asserts that the Hecke operator $T_p$ is equal, as an algebraic correspondence over the special fiber, to the sum of Frobenius and Verschiebung. Blasius and Rogawski proposed a generalization of this result for Shimura varieties with good reduction at $p$, and conjectured that the Frobenius satisfies a certain Hecke polynomial. I will talk about a recent proof of this conjecture for a large class of Shimura varieties of abelian type, and how this proves semisimplicity of cohomology for some Shimura varieties.
Speaker: Si Ying Lee
Institution: Harvard University
Event Organizer: Kartik Prasanna