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The universal Euler characteristic for varieties of characteristic zero

Published online by Cambridge University Press:  04 December 2007

Franziska Bittner
Franziska Bittner
Affiliation:
Mathematisch Instituut, Universiteit Utrecht, The Netherlandsfranziska.bittner@uni-essen.de Universität Essen, FB 6, Mathematik, 45117 Essen, Germany
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Abstract

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Using the weak factorization theorem, we give a simple presentation for the value group of the universal Euler characteristic with compact support for varieties of characteristic zero and describe the value group of the universal Euler characteristic of pairs. This gives a new proof for the existence of natural Euler characteristics with values in the Grothendieck group of Chow motives. A generalization of the presentation to the relative setting allows us to define duality and the six operations.

Keywords

Grothendieck groups of varietiesEuler characteristicweak factorization14E0514F42
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 4 , July 2004 , pp. 1011 - 1032
Copyright
Foundation Compositio Mathematica 2004