Moduli descriptions of v-sheaf local models

Abstract

We propose a uniform moduli-theoretic description of the v-sheaf local model ${\mathbb{M}}_{\mathcal{G},\mu }$ for an arbitrary parahoric group scheme $\mathcal{G}$ and an arbitrary dominant cocharacter $\mu$. Our approach is Tannakian and builds on a new theory of parahoric induced modules. When $\mu$ is minuscule, this framework explains the linear-algebraic conditions arising in the theory of local models of Shimura varieties.

arXiv commentComments welcome!