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arXiv · 1412.7135

Local models for Weil-restricted groups

Brandon Levin
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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 $p \geq 5$. 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.

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Brandon Levin. 2014-12-22. Local models for Weil-restricted groups. https://doi.org/10.1112/s0010437x1600765x

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