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Approximating classifying spaces by smooth projective varieties

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arxiv 0905.1538 v1 pith:XKAPLFC7 submitted 2009-05-11 math.AG math.AT

Torsten Ekedahl This is my paper · ORCID
classification math.AGmath.AT
keywords algebraicclassifyingeverygroupprojectivesmooththeretorsor
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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 $P \to X$ such that the classifying map $X \to \Bclass H$ induces an isomorphism in cohomology in degrees $\le K$. This is then applied to show that if $G$ is a connected non-special group there is a $G$-torsor $P \to X$ for which we do not have $[P]=[G][X]$ in the (completion of the) Grothendieck ring of varieties.

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  1. Integral Weyl Invariants in Chow Characteristic Images of Spin and Special Clifford Groups

    math.AG 2026-07 conditional novelty 7.0 of 10

    Among the recursive Weyl invariants in the Benson–Wood generating sets, only q_3 (Spin(10)) and f_2 (Γ⁺(7)) lie in the Chow characteristic image; all others fail explicit Steenrod tests.

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