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arXiv · 0907.0488

Positive motivic measures are counting measures

Jordan S. Ellenberg·Michael Larsen
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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.

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Jordan S. Ellenberg, Michael Larsen. 2009-07-02. Positive motivic measures are counting measures. https://arxiv.org/abs/0907.0488

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