Gersten Conjecture For Equivariant K-theory And Applications

TL;DR

This paper proves an equivariant version of the Gersten conjecture for reductive group schemes over regular semi-local rings, with applications to representation rings, rigidity, and computations over algebraically closed fields.

Contribution

It introduces an equivariant Gersten conjecture proof for reductive group schemes and explores its implications for K-theory and representation rings.

Findings

Proved equivariant Gersten conjecture for reductive group schemes.

Established rigidity results for equivariant K-theory over henselian local rings.

Computed equivariant K-theory for algebraically closed fields.

Abstract

For a reductive group scheme over a regular semi-local ring, we prove an equivarinat version of the Gersten conjecture. We draw some interesting consequences for the representation rings of such reductive group schemes. We also prove the rigidity for the equivariant K-theory of reductive group schemes over a henselian local ring. This is then used to compute the equivariant K-theory of algebraically closed fields.