Eichler-Shimura relations for Hodge type Shimura varieties

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.

Zoom: https://harvard.zoom.us/j/96767001802

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