Algebraic & Geometric Topology

Characteristic classes of proalgebraic varieties and motivic measures

Shoji Yokura

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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

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

Received: 21 April 2010
Revised: 21 November 2011
Accepted: 19 December 2011
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 18F99: None of the above, but in this section
Secondary: 55N99: None of the above, but in this section 14E18: Arcs and motivic integration 18A99: None of the above, but in this section 55N35: Other homology theories

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


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.

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