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

Abstract

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.

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

References in corpus (2)

• Desingularization of quasi-excellent schemes in characteristic zero
• On the vanishing of negative K-groups

Cited by in corpus (5)

• Algebraic K-theory and descent for blow-ups
• Relative cycles with moduli and regulator maps
• Towards a non-archimedean analytic analog of the Bass-Quillen conjecture
• $K$-theory of monoid algebras and a question of Gubeladze
• Suslin's moving lemma with modulus