Excision, descent, and singularity in algebraic $K$-theory

Abstract

Algebraic $K$-theory is a homology theory that behaves very well on sufficiently nice objects such as stable $C^{\ast }$-algebras or smooth algebraic varieties, and very badly in singular situations. This survey explains how to exploit this to detect singularity phenomena using $K$-theory and cyclic homology.

20 pages. To be presented at the algebra session of ICM 2014. Submitted version

References in corpus (1)

• The K-theory of toric varieties in positive characteristic