A new approach to the geometric Satake equivalence

TL;DR

This paper offers a new proof of the geometric Satake equivalence over separably closed fields and constructs the Galois form of the full L-group using Galois descent.

Contribution

It provides an alternative proof of the geometric Satake equivalence and introduces a canonical Galois form of the L-group.

Findings

New proof of the geometric Satake equivalence

Canonical construction of the Galois form of the L-group

Application of Galois descent in this context

Abstract

I give another proof of the geometric Satake equivalence from Mirkovic-Vilonen over a separably closed field. Using Galois descent, I obtain a canonical construction of the Galois form of the full $L$-group.