On the finite generation of coordinate rings of affine group schemes over discrete valuation rings

TL;DR

This paper proves a finite generation result for the coordinate rings of specific affine group schemes over discrete valuation rings, aiding the simplification of complex geometric Langlands duality proofs.

Contribution

It establishes a finite generation theorem for coordinate rings of affine group schemes over discrete valuation rings, extending the understanding of their algebraic structure.

Findings

Finite generation of coordinate rings proven for certain affine group schemes.

Simplifies the application of Prasad and Yu's results on quasi-reductive groups.

Facilitates progress in geometric Langlands duality studies.

Abstract

In this short note we prove a finite generation result for the coordinate ring of certain affine group schemes over a discrete valuation ring. This may be used to simplify the use of results of Prasad and Yu on quasi-reductive groups by Mirkovic and Vilonen in their work on geometric Langlands duality.