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

Proceedings Mathematical Sciences

Saurav Bhaumik¹ 

[1] School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 00 00, India$$

关键词: Characteristic classes;    étale cohomology;    algebraic stacks.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let $GO(2n)$ be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic $≠ 2$. 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: 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

【 授权许可】

Unknown