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- W3029126790 abstract "We calculate the Grothendieck group $K_0(cal A)$, where $cal A$ is an additive category, locally finite over a Dedekind ring and satisfying some additional conditions. The main examples are categories of modules over finite algebras and the stable homotopy category $mathsf{SW}$ of finite CW-complexes. We show that this group is a direct sum of a free group arising from localizations of the category $cal A$ and a group analogous to the groups of ideal classes of maximal orders. As a corollary, we obtain a new simple proof of the Freyd's theorem describing the group $K_0(mathsf{SW})$." @default.
- W3029126790 created "2020-06-05" @default.
- W3029126790 creator A5065523167 @default.
- W3029126790 date "2020-05-29" @default.
- W3029126790 modified "2023-09-27" @default.
- W3029126790 title "On K_0 of locally finte categories" @default.
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