Extended differential symbol and the Kato homology groups
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911001104875520 |
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| author | Hiranouchi, Toshiro Sugiyama, Rin |
| author_facet | Hiranouchi, Toshiro Sugiyama, Rin |
| contents | Building on our previous work, we investigate an analogue of the differential symbol map used in the Bloch-Gabber-Kato theorem. Within this framework, for an appropriate variety over a field, the higher Chow group corresponds to the 0-th Kato homology group. Inspired by Akhtar's theorem on higher Chow groups, we investigate the structure of the 0-th Kato homology group for varieties over arithmetic fields, including finite fields, local fields, and global fields of positive characteristic. We also express our results in terms of reciprocity sheaves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended differential symbol and the Kato homology groups Hiranouchi, Toshiro Sugiyama, Rin Number Theory 19D45, 14C15 Building on our previous work, we investigate an analogue of the differential symbol map used in the Bloch-Gabber-Kato theorem. Within this framework, for an appropriate variety over a field, the higher Chow group corresponds to the 0-th Kato homology group. Inspired by Akhtar's theorem on higher Chow groups, we investigate the structure of the 0-th Kato homology group for varieties over arithmetic fields, including finite fields, local fields, and global fields of positive characteristic. We also express our results in terms of reciprocity sheaves. |
| title | Extended differential symbol and the Kato homology groups |
| topic | Number Theory 19D45, 14C15 |
| url | https://arxiv.org/abs/2501.11224 |