Toric schemes and integral models for Shimura varieties

Abstract: I will explain a conjectural description of the local structure of $p$-adic integral models for Shimura varieties with level structures "of type $\Gamma_1(p)$”. This aims to generalize a classical result of Deligne-Rapoport about the integral model of the modular curve $X_1(p)$. The description involves two ingredients: A toric scheme which is constructed directly from the local Shimura datum and which is related to the local model of a Shimura variety for parahoric level, and a Galois cover which is a toric extension of the Lang map. This is joint work with M. Rapoport.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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