Positive motivic measures are counting measures
Algebraic Geometry
2009-07-06 v1
Abstract
Let K be a field. A positive motivic measure on the Grothendieck ring K_0(Var_K) is a homomorphism from K_0(Var_K) to the real numbers assigning a nonnegative value to every variety. In this note we show that the only positive motivic measures are the counting measures: measures on K_0(Var_{F_q}) which send a variety to its number of rational points over some fixed finite extension of F_q.
Cite
@article{arxiv.0907.0488,
title = {Positive motivic measures are counting measures},
author = {Jordan S. Ellenberg and Michael Larsen},
journal= {arXiv preprint arXiv:0907.0488},
year = {2009}
}
Comments
5 pages