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An
additive variant of the differential symbol maps
Toshiro Hiranouchi |
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Vol. 9 (2024), No. 3, 499–518
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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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Authors |
| Toshiro Hiranouchi | |
| Graduate School of Engineering,
Department of Basic Sciences Kyushu Institute of Technology Kitakyushu 804-8550 Japan |
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| © 2024 MSP (Mathematical Sciences Publishers). |
