Chern classes of proalgebraic varieties and motivic measures
| dc.creator | Yokura, Shoji | |
| dc.date | 2004-07-14 | |
| dc.date.accessioned | 2026-07-07T05:10:17Z | |
| dc.date.available | 2026-07-07T05:10:17Z | |
| dc.description | 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 construct Chern--Schwartz--MacPherson classes of proalgebraic varieties, by introducing the notion of ``proconstructible functions " and "$χ$-stable proconstructible functions" and using the Fulton-MacPherson's Bivariant Theory. As a "motivic" version of a $χ$-stable proconstructible function, $\Ga$-stable constructible functions are introduced. This construction naturally generalizes the so-called motivic measure and motivic integration. For the Nash arc space $\Cal L(X)$ of an algebraic variety $X$, the proconstructible set is equivalent to the so-called cylinder set or constructible set in the arc space. | |
| dc.description | 37 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407237 | |
| dc.identifier | http://arxiv.org/abs/math/0407237 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71882 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.subject | 14C17, 14F99, 55N35 | |
| dc.title | Chern classes of proalgebraic varieties and motivic measures | |
| dc.type | text |