Eichler-Shimura relations of 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 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 for some Shimura varieties of Hodge type.

number theory

Audience: researchers in the topic

London number theory seminar

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