Volume 12, issue 1 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Characteristic classes of proalgebraic varieties and motivic measures

Shoji Yokura

Algebraic & Geometric Topology 12 (2012) 601–641
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.

Dedicated to Clint McCrory on the occasion of his 65th birthday

Keywords
characteristic class of singular variety, Fulton–MacPherson bivariant theory, relative Grothendieck group of variety, motivic measure, proalgebraic variety
Mathematical Subject Classification 2000
Primary: 14C17, 18F99
Secondary: 55N99, 14E18, 18A99, 55N35
References
Publication
Received: 21 April 2010
Revised: 21 November 2011
Accepted: 19 December 2011
Published: 8 April 2012
Authors
Shoji Yokura
Department of Mathematics and Computer Science
Faculty of Science
Kagoshima University
1-21-35 Korimoto 1-chome
Kagoshima 890-0065
Japan