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

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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Milnor $K$-theory, Gersten complex
Mathematical Subject Classification
Primary: 19D45
Secondary: 14F20, 14F42
Received: 12 October 2021
Revised: 8 April 2022
Accepted: 24 April 2022
Published: 20 August 2022
Rakesh Pawar
Department of Mathematics
Indian Institute of Science and Education Research, Mohali
Department of Mathematical Sciences
Indian Institute of Science Education and Research, Pune