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Nearby cycles for local models of some Shimura varieties. (English) Zbl 1009.11042

The authors solved a Kottwitz’s conjecture, which is a formula for the semisimple trace for the Frobenius acting on the nearby cycles of a local model at \(p\) of a Shimura variety with prescribed level structure of Iwahori type at \(p\). Such a computation is important for determining the local factor at \(p\) of the semisimple Hasse-Weil zeta-function of the Shimura variety. It is a surprising and interesting fact that some ideas used by the authors come from the geometric Langlands program, especially from Beilinson and Gaitsgory.

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
20C08 Hecke algebras and their representations
14M15 Grassmannians, Schubert varieties, flag manifolds
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