2012/01/23 by Saurav Bhaumik, Bhaumik, Saurav
Mathematics · #14F20 #14L30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14F20 #msc:14L30
paper · pdf · doi:10.48550/arxiv.1201.4628
9 pages
arxiv created 2012/01/23 · openalex publication_date 2012/01/23 · arxiv updated 2012/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let GO(2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic not equal to 2. We determine the etale cohomology ring with mod 2 coefficients of the algebraic stack BGO(2n). In the topological category, Y. Holla and N. 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 etale 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 Gm fibration BO(2n) to BGO(2n) of algebraic stacks.