Eichler-Shimura relations

Algebra and Number Theory Seminar
Event time: 
Tuesday, February 15, 2022 - 4:30pm
Si Ying Lee
Speaker affiliation: 
Event description: 

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.