Local models for Weil-restricted groups. (27th September 2016) - Levin, Brandon
Abstract : We extend the group-theoretic construction of local models of Pappas and Zhu [ Local models of Shimura varieties and a conjecture of Kottwitz, Invent. Math.194 (2013), 147–254] 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 $p\geqslant 5$ . 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.