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An additive variant of the differential symbol maps

Toshiro Hiranouchi

Vol. 9 (2024), No. 3, 499–518
Abstract

Our investigation focuses on an additive analogue of the Bloch–Gabber–Kato theorem which establishes a relation between the Milnor K-group of a field of positive characteristic and a Galois cohomology group of the field. Extending the Artin–Schreier–Witt theory, we present an isomorphism from the Mackey product associated with the Witt group and the multiplicative groups to a Galois cohomology group. As a result, we give a new expression for the torsion subgroup of the Brauer group of a field, and more generally, the Kato homology groups.

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Keywords
Milnor $K$-group, Kähler differential
Mathematical Subject Classification
Primary: 19C30, 19D45
Milestones
Received: 1 April 2024
Revised: 17 June 2024
Accepted: 3 July 2024
Published: 28 August 2024
Authors
Toshiro Hiranouchi
Graduate School of Engineering, Department of Basic Sciences
Kyushu Institute of Technology
Kitakyushu 804-8550
Japan