arXiv · 2410.13534
We construct a fundamental theory of the derived category of non-finite bi-filtered complexes.
Yukiyoshi Nakkajima. 2024-10-17. Derived categories of bifiltered complexes. https://arxiv.org/abs/2410.13534
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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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