Characteristic classes of proalgebraic varieties and motivic measures

Yokura, Shoji

doi:10.2140/agt.2012.12.601

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Characteristic classes of proalgebraic varieties and motivic measures

Shoji Yokura

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.

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

Volume 12, issue 1 (2012)