论文标题
$ e_ \ infty $ -cells和无限字段的一般线性群
$E_\infty$-cells and general linear groups of infinite fields
论文作者
论文摘要
我们从$ e_ \ infty $ - 代数的角度研究了无限场（或更一般连接的半局部环与无限残留场的半局部环环）的一般线性群。我们证明，对于$ e_ \ infty $ - 知识分子，坡度2的消失线消失了，并通过确定Steinberg模块上的所有不变双线性形式来分析该行上的组。我们从这一后果中得出了许多有关通用线性群体不稳定同源性的后果，特别是回答了Rognes，Suslin，Mirzaii等问题。
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.
