Work

$E_\infty$-cells and general linear groups of infinite fields

Year: 2020

Type: preprint

Abstract: 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2005.05620

Authors: Galatius, Soren, Kupers, Alexander, Randal-Williams, Oscar

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4394638756

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