Characteristic classes of proalgebraic varieties and motivic measures

Yokura, Shoji¹

¹Department of Mathematics and Computer Science, Faculty of Science, Kagoshima University, 1-21-35 Korimoto 1-chome, Kagoshima 890-0065, Japan

Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 601-641

Résumé

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.

Détail

DOI : 10.2140/agt.2012.12.601

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

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