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Abstract
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Our investigation focuses on an additive analogue of the
Bloch–Gabber–Kato theorem which establishes a relation between the Milnor
-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
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Mathematical Subject Classification
Primary: 19C30, 19D45
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Milestones
Received: 1 April 2024
Revised: 17 June 2024
Accepted: 3 July 2024
Published: 28 August 2024
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