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Approximating classifying spaces by smooth projective varieties

2009/05/11 by Torsten Ekedahl, Ekedahl, Torsten
Mathematics · #14F25 #14L24 #55R40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #math.AT #msc:14F25 #msc:14L24 #msc:55R40

paper · pdf · doi:10.48550/arxiv.0905.1538

9 pages

arxiv created 2009/05/11 · openalex publication_date 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for every reductive algebraic group H with centre of positive dimension and every integer K there is a smooth and projective variety X and an algebraic H-torsor P → X such that the classifying map X → \Bclass H induces an isomorphism in cohomology in degrees ≤ K. This is then applied to show that if G is a connected non-special group there is a G-torsor P → X for which we do not have [P]=[G][X] in the (completion of the) Grothendieck ring of varieties.

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