Milnor-Witt motivic cohomology and linear algebraic groups

Publication date: 8 June 2023

Abstract: This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups

S p_{2 n}

for any

n i n m a t h b b N

using the

S p

-orientation and the associated Borel classes. Secondly, following the classical computations and using the analogue in

m a t h b b A^{1}

-homotopy of the Leray spectral sequence, we compute the

e t a

-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the

e t a

-inverted MW motivic cohomology of the general linear groups

G L_{n}

and special linear groups

S L_{n}

for any

n i n m a t h b b N

.

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