$E_\infty$-cells and general linear groups of infinite fields
| Autor: | Galatius, Soren, Kupers, Alexander, Randal-Williams, Oscar |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 84 pages; v2 minor revision |
| Databáze: | arXiv |
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