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Characteristic classes for GO(2n) in étale cohomology
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bhaumik, Saurav |
| Copyright Year | 2012 |
| Abstract | Let $GO(2n)$ be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic $\ne 2$. 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. |
| Starting Page | 225 |
| Ending Page | 233 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s12044-013-0121-z |
| Volume Number | 123 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1201.4628v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s12044-013-0121-z |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
