The motivic Satake equivalence using perverse Nori motives

TL;DR

This paper develops a refined motivic version of the geometric Satake equivalence using stratified perverse Nori motives, providing a new perspective beyond the existing Tate motivic approach.

Contribution

It introduces the theory of stratified perverse Nori motives and establishes a Nori motivic Satake equivalence, advancing the understanding of geometric representation theory in a motivic framework.

Findings

Established the Nori motivic Satake equivalence.

Refined the geometric Satake equivalence using Nori motives.

Differentiated between Tate and Nori motivic approaches.

Abstract

In this article, we develop the theory of stratified perverse Nori motives to prove a refinement of the geometric Satake equivalence of Mirkovi\'c-Vilonen, for which we call the Nori motivic Satake equivalence, in contrast to the "Tate motivic" Satake equivalence of Richarz-Scholbach.