English

Pro cdh-descent for cyclic homology and $K$-theory

K-Theory and Homology 2019-02-20 v3 Algebraic Geometry

Abstract

In this paper we prove that cyclic homology, topological cyclic homology, and algebraic KK-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 KK-theory with compact support.

Keywords

Cite

@article{arxiv.1211.1813,
  title  = {Pro cdh-descent for cyclic homology and $K$-theory},
  author = {Matthew Morrow},
  journal= {arXiv preprint arXiv:1211.1813},
  year   = {2019}
}

Comments

This is a substantial replacement of the earlier version, whose contents have been expanded and divided into three disjoint papers: arXiv:1404.4179, the current paper, and arXiv:1404.4649. In particular, the proof of pro cdh-descent of $K$-theory has been extended to finite characteristic