Characteristic classes of proalgebraic varieties and motivic measures

Details Characteristic classes of proalgebraic varieties and motivic measures Characteristic classes of proalgebraic varieties and motivic measures

2006-06-15

arxiv.org/abs/math/0606352v2

Mathematics

Algebraic Geometry

a revised version of math.AG/0407237

Scientific paper

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--Poincar\'e characteristic with values in the Grothendieck ring is a generalization of the so-called motivic measure.

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