Characteristic classes of proalgebraic varieties and motivic measures
Abstract
Michael Gromov has recently initiated what he calls ``symbolic algebraic geometry", in which objects are proalgebraic varieties: a proalgebraic variety is by definition the projective limit of a projective system of algebraic varieties. In this paper we introduce characteristic classes of proalgebraic varieties, using Grothendieck transformations of Fulton--MacPherson's Bivariant Theory, modeled on the construction of MacPherson's Chern class transformation of proalgebraic varieties. We show that a proalgebraic version of the Euler--Poincaré characteristic with values in the Grothendieck ring is a generalization of the so-called motivic measure.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2006
- DOI:
- 10.48550/arXiv.math/0606352
- arXiv:
- arXiv:math/0606352
- Bibcode:
- 2006math......6352Y
- Keywords:
-
- Mathematics - Algebraic Geometry;
- Mathematics - Algebraic Topology;
- 14C17;
- 14F99;
- 55N35
- E-Print:
- a revised version of math.AG/0407237