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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality 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 1.43.

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Nil $K$-theory maps to cyclic homology
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by Charles A. Weibel PDF
Trans. Amer. Math. Soc. 303 (1987), 541-558 Request permission

Abstract:

Algebraic $K$-theory breaks into two pieces: nil $K$-theory and Karoubi-Villamayor $K$-theory. Karoubi has constructed Chern classes from the latter groups into cyclic homology. We construct maps from nil $K$-theory to cyclic homology which are compatible with Karoubi’s maps, but with a degree shift. Several recent results show that in characteristic zero our map is often an isomorphism.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 303 (1987), 541-558
  • MSC: Primary 18F25; Secondary 18G99, 19D35, 19D55
  • DOI: https://doi.org/10.1090/S0002-9947-1987-0902784-0
  • MathSciNet review: 902784