# Eichler-Shimura relations

## Location

Zoom

Event Series

Event Type

Seminar

Monday, February 7, 2022 12:30 PM

Si Ying Lee (Harvard)

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 which satisfy a Hodge-Newton decomposability condition.