An additive variant of the differential symbol maps
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916378474184704 |
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| author | Hiranouchi, Toshiro |
| author_facet | Hiranouchi, Toshiro |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An additive variant of the differential symbol maps Hiranouchi, Toshiro K-Theory and Homology Number Theory 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. |
| title | An additive variant of the differential symbol maps |
| topic | K-Theory and Homology Number Theory |
| url | https://arxiv.org/abs/2403.19974 |