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PRO CDH-DESCENT FOR CYCLIC HOMOLOGY AND $K$-THEORY

Part of: Higher algebraic $K$-theory Commutative algebra: Homological methods

Published online by Cambridge University Press:  27 November 2014

Matthew Morrow
Matthew Morrow*
Affiliation:
Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (morrow@math.uni-bonn.de)http://www.math.uni-bonn.de/people/morrow/
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Abstract

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In this paper, we prove that cyclic homology, topological cyclic homology, and algebraic $K$-theory satisfy a pro Mayer–Vietoris property with respect to abstract blow-up squares of varieties, in both zero and finite characteristic. This may be interpreted as the well-definedness of $K$-theory with compact support.

Keywords

K-theorycyclic homologycdh-topology

MSC classification

Primary: 19D55: $K$-theory and homology; cyclic homology and cohomology
Secondary: 13D03: (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 15 , Issue 3 , July 2016 , pp. 539 - 567
Copyright
© Cambridge University Press 2014 

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