A remark on the Gersten complex for Milnor $K$-theory

Rakesh Pawar

Vol. 318 (2022), No. 2, 295–304

DOI: 10.2140/pjm.2022.318.295

Abstract

We consider the Gersten complex for Milnor $K$-theory over a regular local Henselian domain $S$ and prove that in degrees $\ge \dim <!--FUNCTION\; APPLICATION-->S\ge 1$, the Gersten complex of an essentially smooth Henselian local $S$-scheme is exact.

Keywords

Milnor $K$-theory, Gersten complex

Mathematical Subject Classification

Primary: 19D45

Secondary: 14F20, 14F42

Milestones

Received: 12 October 2021

Revised: 8 April 2022

Accepted: 24 April 2022

Published: 20 August 2022