Fixed points under pinning-preserving automorphisms of reductive group schemes

Pramod N. Achar (1) , Timo Richarz (2) , Simon Riche (3) , João Lourenço (4)

1 Department of Mathematics Louisiana State University
2 TU Darmstadt - Technische Universität Darmstadt - Technical University of Darmstadt
3 LMBP - Laboratoire de Mathématiques Blaise Pascal
4 WWU - Westfälische Wilhelms-Universität Münster = University of Münster

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.

Domaines: Théorie des représentations [math.RT]

Pramod N. Achar, Timo Richarz, Simon Riche, João Lourenço. Fixed points under pinning-preserving automorphisms of reductive group schemes. 2023. ⟨hal-03919246⟩