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.


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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