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Stable cohomology of congruence subgroups

Published 3 Mar 2022 in math.AT, math.GR, math.KT, and math.NT | (2203.01697v1)

Abstract: We describe the $\mathbb{F}_p$-cohomology of the congruence subgroups $SL_n(\mathbb{Z}, pm)$ in degrees $* < p$, 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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