KV-theory of categories
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- by Charles A. Weibel PDF
- Trans. Amer. Math. Soc. 267 (1981), 621-635 Request permission
Abstract:
Quillen has constructed a $K$-theory ${K_{\ast }}C$ for nice categories, one of which is the category of projective $R$-modules. We construct a theory $K{V_{\ast }}C$ for the nice categories parametrized by rings. When applied to projective modules we recover the Karoubi-Villamayor $K$-theory $K{V_{\ast }}(R)$. As an application, we show that the Cartan map from ${K_{\ast }}(R)$ to ${G_{\ast }}(R)$ factors through the groups $K{V_{\ast }}(R)$. We also compute $K{V_{\ast }}$ for the categories of faithful projectives and Azumaya algebras, generalizing results of Bass.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 267 (1981), 621-635
- MSC: Primary 18F25
- DOI: https://doi.org/10.1090/S0002-9947-1981-0626494-7
- MathSciNet review: 626494