Algebraic & Geometric Topology 12 (2012) 601–641

DOI: 10.2140/agt.2012.12.601

Abstract

Gromov initiated what he calls “symbolic algebraic geometry”, in which he studied proalgebraic varieties. In this paper we formulate a general theory of characteristic classes of proalgebraic varieties as a natural transformation, which is a natural extension of the well-studied theories of characteristic classes of singular varieties. Fulton–MacPherson bivariant theory is a key tool for our formulation and our approach naturally leads us to the notion of motivic measure and also its generalization.

Keywords

characteristic class of singular variety, Fulton–MacPherson bivariant theory, relative Grothendieck group of variety, motivic measure, proalgebraic variety

Mathematical Subject Classification

Primary: 14C17, 18F99

Secondary: 14E18, 18A99, 55N35, 55N99

References

Publication

Received: 21 April 2010
Revised: 21 November 2011
Accepted: 19 December 2011
Published: 8 April 2012

Authors