## Algebraic & Geometric Topology

### Characteristic classes of proalgebraic varieties and motivic measures

Shoji Yokura

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 12, Number 1 (2012), 601-641.

Dates
Revised: 21 November 2011
Accepted: 19 December 2011
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715351

Digital Object Identifier
doi:10.2140/agt.2012.12.601

Mathematical Reviews number (MathSciNet)
MR2916288

Zentralblatt MATH identifier
1243.14010

#### Citation

Yokura, Shoji. Characteristic classes of proalgebraic varieties and motivic measures. Algebr. Geom. Topol. 12 (2012), no. 1, 601--641. doi:10.2140/agt.2012.12.601. https://projecteuclid.org/euclid.agt/1513715351

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