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2010 Positive motivic measures are counting measures
Jordan Ellenberg, Michael Larsen
Algebra Number Theory 4(1): 105-109 (2010). DOI: 10.2140/ant.2010.4.105

Abstract

A motivic measure is a ring homomorphism from the Grothendieck group of a field K (with multiplication coming from the fiber product over SpecK) to some field. We show that if a real-valued motivic measure μ satisfies μ([V])0 for all K-varieties V, then μ is a counting measure; that is, there exists a finite field L containing K such that μ([V])=|V(L)| for all K-varieties V.

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Jordan Ellenberg. Michael Larsen. "Positive motivic measures are counting measures." Algebra Number Theory 4 (1) 105 - 109, 2010. https://doi.org/10.2140/ant.2010.4.105

Information

Received: 10 July 2009; Accepted: 10 August 2009; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1196.14021
MathSciNet: MR2592015
Digital Object Identifier: 10.2140/ant.2010.4.105

Subjects:
Primary: 14F43
Secondary: 14G15

Keywords: finite fields , motives , motivic measures

Rights: Copyright © 2010 Mathematical Sciences Publishers

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