1 results
Local models for Weil-restricted groups
- Part of
-
- Journal:
- Compositio Mathematica / Volume 152 / Issue 12 / December 2016
- Published online by Cambridge University Press:
- 27 September 2016, pp. 2563-2601
- Print publication:
- December 2016
-
- Article
-
- You have access
- Export citation
-
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.
