Motivic cohomology of the Nisnevich classifying space of even Clifford groups

Fabio Tanania

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arXiv · 2302.04772

Motivic cohomology of the Nisnevich classifying space of even Clifford groups

Fabio Tanania

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Abstract

In this paper, we consider the split even Clifford group $\Gamma^+_n$ and compute the mod 2 motivic cohomology ring of its Nisnevich classifying space. The description we obtain is quite similar to the one provided for spin groups in [11]. The fundamental difference resides in the behaviour of the second subtle Stiefel-Whitney class that is non-trivial for even Clifford groups, while it vanished in the spin-case.

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Fabio Tanania. 2023-02-09. Motivic cohomology of the Nisnevich classifying space of even Clifford groups. https://arxiv.org/abs/2302.04772

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