Positive motivic measures are counting measures

Details Positive motivic measures are counting measures Positive motivic measures are counting measures

2009-07-02

arxiv.org/abs/0907.0488v1

Mathematics

Algebraic Geometry

5 pages

Scientific paper

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.

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