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arXiv · 2609.09871

The Oka principle for \'etale Chow groups

Ko Aoki
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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 \'etale (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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Ko Aoki. 2026-09-09. The Oka principle for \'etale Chow groups. https://arxiv.org/abs/2609.09871

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