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arXiv 2203.016972022-03math.ATmath.GRmath.KTmath.NT

同余子群的稳定上同调

Stable cohomology of congruence subgroups

Centre for Mathematical Sciences（数学科学中心）

Oscar Randal-Williams

备注：: 40 pages; v2 accepted version, to appear in Compositio Mathematica

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AI总结：

研究同余子群SL_n(Z,p^m)在度数小于p-1时的F_p上同调，提出并验证了Calegari的公式，同时推导了SL_n(Z/p)在特定扭曲系数下的稳定上同调公式。

摘要：

我们描述了同余子群SL_n(Z,p^m)在度数* < p-1时的F_p上同调，对于足够大的n，建立了Calegari提出的公式。在此过程中，我们还推导了SL_n(Z/p)在某些扭曲系数下的稳定上同调公式。

英文摘要：

We describe the $\mathbb{F}_p$-cohomology of the congruence subgroups $SL_n(\mathbb{Z}, p^m)$ in degrees $* < p-1$, for all large enough $n$, establishing a formula proposed by F. Calegari. Along the way, we also establish a formula for the stable cohomology of $SL_n(\mathbb{Z}/p)$ with certain twisted coefficients.

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