In this paper, we consider the split even Clifford group [Formula Present] 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 [Math. Z. 301 (2022), no. 1, 41–74]. The fundamental difference resides in the behaviour of the second subtle Stiefel–Whitney class that is non-trivial for even Clifford groups, while it vanishes in the spin-case.
Tanania, F. (2024). Motivic cohomology of the Nisnevich classifying space of even Clifford groups. DOCUMENTA MATHEMATICA, 29(1), 191-208 [10.4171/DM/931].
Motivic cohomology of the Nisnevich classifying space of even Clifford groups
Tanania F.
2024
Abstract
In this paper, we consider the split even Clifford group [Formula Present] 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 [Math. Z. 301 (2022), no. 1, 41–74]. The fundamental difference resides in the behaviour of the second subtle Stiefel–Whitney class that is non-trivial for even Clifford groups, while it vanishes in the spin-case.
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