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arXiv · 2501.11224

Extended differential symbol and the Kato homology groups

Toshiro Hiranouchi·Rin Sugiyama
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Abstract

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.

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Toshiro Hiranouchi, Rin Sugiyama. 2025-01-20. Extended differential symbol and the Kato homology groups. https://arxiv.org/abs/2501.11224

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