Milnor-Witt motivic cohomology and linear algebraic groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913616773513216 |
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| 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 |