Local Gersten's conjecture for regular system of parameters

TL;DR

This paper proves the local Gersten's conjecture for regular systems of parameters, leading to the validation of Gersten's conjecture for certain regular local rings and smooth rings over discrete valuation rings.

Contribution

It establishes the local Gersten's conjecture for regular systems of parameters, extending the conjecture's validity to broader classes of rings.

Findings

Proves local Gersten's conjecture for regular systems of parameters.

Derives Gersten's conjecture for regular local rings.

Validates Gersten's conjecture for smooth rings over discrete valuation rings.

Abstract

In this paper, we show local Gersten's conjecture for regular system of parameters. As its consequence we obtain Gersten's conjecture for a commutative regular local ring and smooth over a commutative discrete valuation ring.