Vol. 318, No. 2, 2022
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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 ≥ dim ⁡ S ≥ 1, the Gersten complex of an essentially smooth Henselian local S-scheme is exact.

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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
Authors
Rakesh Pawar
Department of Mathematics
Indian Institute of Science and Education Research, Mohali
Mohali
India		 Department of Mathematical Sciences
Indian Institute of Science Education and Research, Pune
Pune
India