Milnor-Witt motivic cohomology and linear algebraic groups

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autore principale: Peng, Keyao
Natura: Preprint
Pubblicazione: 2023
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866913616773513216
author Peng, Keyao
author_facet Peng, Keyao
contents This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups $Sp_{2n}$ for any $n\in\mathbb{N}$ using the $Sp$-orientation and the associated Borel classes. Secondly, following the classical computations and using the analogue in $\mathbb{A}^1$-homotopy of the Leray spectral sequence, we compute the $η$-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the $η$-inverted MW-motivic cohomology of the general linear groups $GL_n$ and the special linear groups $SL_n$ for any $n\in\mathbb{N}$. Finally, we determine the multiplicative structures of these total cohomology groups.
format Preprint
id arxiv_https___arxiv_org_abs_2306_05260
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Milnor-Witt motivic cohomology and linear algebraic groups
Peng, Keyao
Algebraic Geometry
This article presents two key computations in MW-motivic cohomology. Firstly, we compute the MW-motivic cohomology of the symplectic groups $Sp_{2n}$ for any $n\in\mathbb{N}$ using the $Sp$-orientation and the associated Borel classes. Secondly, following the classical computations and using the analogue in $\mathbb{A}^1$-homotopy of the Leray spectral sequence, we compute the $η$-inverted MW-motivic cohomology of general Stiefel varieties, obtaining in particular the computation of the $η$-inverted MW-motivic cohomology of the general linear groups $GL_n$ and the special linear groups $SL_n$ for any $n\in\mathbb{N}$. Finally, we determine the multiplicative structures of these total cohomology groups.
title Milnor-Witt motivic cohomology and linear algebraic groups
topic Algebraic Geometry
url https://arxiv.org/abs/2306.05260