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Transactions of the American Mathematical Society

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

 
 

 

Nil $K$-theory maps to cyclic homology


Author: Charles A. Weibel
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
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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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Keywords: Cyclic homology, algebraic <IMG WIDTH="24" HEIGHT="18" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$K$">-theory
Article copyright: © Copyright 1987 American Mathematical Society