Excision, descent, and singularity in algebraic K-theory

2013/12/05 by Cortiñas, Guillermo
#19E08 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #Primary 19D55 #Secondary 19D50

paper · doi:10.48550/arxiv.1312.1639

Abstract

Algebraic K-theory is a homology theory that behaves very well on sufficiently nice objects such as stable C^*-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.

Related

• Algebraic K-Theory
• Applications of topological cyclic homology to algebraic K-theory
• A Quick Overview On Regular Algebraic K-Theory For Groups
• Algebraic K-theory with coefficients of cyclic quotient singularities
• Twisted K-homology theory, twisted Ext-theory