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Bibliographic Details
Main Authors: Galatius, Soren, Kupers, Alexander, Randal-Williams, Oscar
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2005.05620
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Table of 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.