Local models for Weil-restricted groups

Abstract

We extend the group theoretic construction of local models of Pappas and Zhu to the case of groups obtained by Weil restriction along a possibly wildly ramified extension. This completes the construction of local models for all reductive groups when $p\ge 5$. We show that the local models are normal with special fiber reduced and study the monodromy action on the sheaves of nearby cycles. As a consequence, we prove a conjecture of Kottwitz that the semi-simple trace of Frobenius gives a central function in the parahoric Hecke algebra. We also introduce a notion of splitting model and use this to study the inertial action in the case of an unramified group.

References in corpus (1)

• On parahoric subgroups

Cited by in corpus (7)

• Algebraic families of Galois representations and potentially semi-stable pseudodeformation rings
• The intersection motive of the moduli stack of shtukas
• The Test Function Conjecture for Local Models of Weil-restricted groups
• On integral models of Shimura varieties
• Good and semi-stable reductions of Shimura varieties
• Independence of $\ell$ for Frobenius conjugacy classes attached to abelian varieties
• On integral local Shimura varieties