Odd rank vector bundles in eta-periodic motivic homotopy theory
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914039234297856 |
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| author | Haution, Olivier |
| author_facet | Haution, Olivier |
| contents | We observe that, in the eta-periodic motivic stable homotopy category, odd rank vector bundles behave to some extent as if they had a nowhere vanishing section. We discuss some consequences concerning SLc-orientations of motivic ring spectra, and the etale classifying spaces of certain algebraic groups. In particular, we compute the classifying spaces of diagonalisable groups in the eta-periodic motivic stable homotopy category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_06021 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Odd rank vector bundles in eta-periodic motivic homotopy theory Haution, Olivier Algebraic Geometry K-Theory and Homology We observe that, in the eta-periodic motivic stable homotopy category, odd rank vector bundles behave to some extent as if they had a nowhere vanishing section. We discuss some consequences concerning SLc-orientations of motivic ring spectra, and the etale classifying spaces of certain algebraic groups. In particular, we compute the classifying spaces of diagonalisable groups in the eta-periodic motivic stable homotopy category. |
| title | Odd rank vector bundles in eta-periodic motivic homotopy theory |
| topic | Algebraic Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2203.06021 |