The universal Euler characteristic for varieties of characteristic zero

2001/11/06 by Franziska Bittner, Bittner, Franziska · 6 citations
Computer Science · Mathematics · #14E05 #14F42 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E05 #msc:14F42

paper · pdf · doi:10.48550/arxiv.math/0111062

19 pages

arxiv created 2001/11/06 · openalex publication_date 2001/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• The \mathbbA¹-Euler characteristic of symmetric powers
• Involution on the Graded Grothendieck Ring of Varieties and \mathbbD-Singularities
• The quantum D-module of product varieties
• Singularities of symmetric powers and irrationality of motivic zeta functions
• Relative Mather discrepancy on arc spaces
• Does the Grothendieck ring of varieties contain nilpotent elements?

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