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    The Chow ring for the classifying space of GO(2n)GO(2n)

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    Let GO(2n)GO(2n) be the general orthogonal group scheme (the group of orthogonal similitudes). In the topological category, Y. Holla and N. Nitsure determined the singular cohomology ring Hsing(BGO(2n,C),F2)H^*_{\rm sing}(BGO(2n,\mathbb C),\mathbb F_2) of the classifying space BGO(2n,C)BGO(2n,\mathbb C) of the corresponding complex Lie group GO(2n,C)GO(2n,\mathbb C) in terms of explicit generators and relations. The author of the present note showed that over any algebraically closed field of characteristic not equal to 22, the smooth-\'etale cohomology ring Hsmeˊt(BGO(2n),F2)H_{\rm sm-\'et}^*(BGO(2n),\mathbb F_2) of the classifying algebraic stack BGO(2n)BGO(2n) has the same description in terms of generators and relations as the singular cohomology ring Hsing(BGO(2n,C),F2)H^*_{\rm sing}(BGO(2n,\mathbb C),\mathbb F_2). Totaro defined for any reductive group GG over a field, the Chow ring AGA^*_G, which is canonically identified with the ring of characteristic classes in the sense of intersection theory, for principal GG-bundles, locally trivial in \'etale topology. In this paper, we calculate the Chow group AGO(2n)A^*_{GO(2n)} over any field of characteristic different from 22 in terms of generators and relations.Comment: 11 page

    The Chow ring of the classifying space of GO(2n)

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