Eichler-Shimura relations for Hodge type Shimura varieties

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 Verschebung. Blasius and Rogawski proposed a generalization of this result for general 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 Shimura varieties of Hodge type, assuming a technical condition on the unramified sigma-conjugacy classes in the associated Kottwitz set.

number theory

Audience: researchers in the topic

Harvard number theory seminar