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The Oka principle for étale Chow groups
Abstract
The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative complex Banach algebra. In his 1974 ICM address, Taylor asked whether the higher cohomology groups admit descriptions in terms of the underlying ring. We give a solution to this question in even degrees: The étale (aka Lichtenbaum) Chow group in every codimension is canonically isomorphic to the corresponding even integral cohomology group of the Gelfand spectrum.
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BibTeX
@misc{aoki2026principle,
title = {{The Oka principle for étale Chow groups}},
author = {Ko Aoki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09871},
eprint = {2609.09871},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09871},
}
RIS
TY - UNPB
TI - The Oka principle for étale Chow groups
AU - Ko Aoki
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09871
UR - https://arxiv.org/abs/2609.09871
AB - The celebrated theorems of Shilov, Arens--Royden, and Forster give direct descriptions of the first three integral cohomology groups of the Gelfand spectrum of a commutative complex Banach algebra. In his 1974 ICM address, Taylor asked whether the higher cohomology groups admit descriptions in terms of the underlying ring. We give a solution to this question in even degrees: The étale (aka Lichtenbaum) Chow group in every codimension is canonically isomorphic to the corresponding even integral cohomology group of the Gelfand spectrum.
ER -