Fixed points under pinning-preserving automorphisms of reductive group schemes

TL;DR

This paper characterizes the fixed points of automorphisms on reductive group schemes, providing foundational results for a subsequent work on ramified geometric Satake equivalence with integral or modular coefficients.

Contribution

It determines the scheme-theoretic fixed points of pinned reductive group schemes under automorphisms that preserve the pinning, advancing the understanding of their structure.

Findings

Identification of fixed point schemes under automorphisms

Application to ramified geometric Satake equivalence

Foundation for modular coefficient theories

Abstract

In this paper we determine the scheme-theoretic fixed points of pinned reductive group schemes acted upon by a group of pinning-preserving automorphisms. The results are used in a companion paper to establish a ramified geometric Satake equivalence with integral or modular coefficients.