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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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