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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2005.05620 |
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| _version_ | 1866929680838295552 |
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| author | Galatius, Soren Kupers, Alexander Randal-Williams, Oscar |
| author_facet | Galatius, Soren Kupers, Alexander Randal-Williams, Oscar |
| contents | We study the general linear groups of infinite fields (or more generally connected semi-local rings with infinite residue fields) from the perspective of $E_\infty$-algebras. We prove that there is a vanishing line of slope 2 for their $E_\infty$-homology, and analyse the groups on this line by determining all invariant bilinear forms on Steinberg modules. We deduce from this a number of consequences regarding the unstable homology of general linear groups, in particular answering questions of Rognes, Suslin, Mirzaii, and others. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_05620 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $E_\infty$-cells and general linear groups of infinite fields Galatius, Soren Kupers, Alexander Randal-Williams, Oscar Algebraic Topology K-Theory and Homology 18F25, 20G15, 55P48 We study the general linear groups of infinite fields (or more generally connected semi-local rings with infinite residue fields) from the perspective of $E_\infty$-algebras. We prove that there is a vanishing line of slope 2 for their $E_\infty$-homology, and analyse the groups on this line by determining all invariant bilinear forms on Steinberg modules. We deduce from this a number of consequences regarding the unstable homology of general linear groups, in particular answering questions of Rognes, Suslin, Mirzaii, and others. |
| title | $E_\infty$-cells and general linear groups of infinite fields |
| topic | Algebraic Topology K-Theory and Homology 18F25, 20G15, 55P48 |
| url | https://arxiv.org/abs/2005.05620 |