Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 12, Number 1 (2012), 601-641.
Characteristic classes of proalgebraic varieties and motivic measures
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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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
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