• Characteristic Classes for $GO(2n)$ in étale Cohomology

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      https://www.ias.ac.in/article/fulltext/pmsc/123/02/0225-0233

    • Keywords

       

      Characteristic classes; étale cohomology; algebraic stacks.

    • Abstract

       

      Let $GO(2n)$ be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic $\neq 2$. We determine the smooth-étale cohomology ring with $\mathbb{F}_2$ coefficients of the algebraic stack $BGO(2n)$. In the topological category, Holla and Nitsure determined the singular cohomology ring of the classifying space $BGO(2n)$ of the complex Lie group $GO(2n)$ in terms of explicit generators and relations. We extend their results to the algebraic category. The chief ingredients in this are: (i) an extension to étale cohomology of an idea of Totaro, originally used in the context of Chow groups, which allows us to approximate the classifying stack by quasi projective schemes; and (ii) construction of a Gysin sequence for the $\mathbb{G}_m$-fibration $BO(2n)\to BGO(2n)$ of algebraic stacks.

    • Author Affiliations

       

      Saurav Bhaumik1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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