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arXiv · 2403.19974

An additive variant of the differential symbol maps

Toshiro Hiranouchi
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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 Aritin-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 an expression for the torsion subgroup of the Brauer group of a field, and more generally, the Kato homology groups.

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Toshiro Hiranouchi. 2024-03-29. An additive variant of the differential symbol maps. https://doi.org/10.2140/akt.2024.9.499

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