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arXiv · 2410.08933

Profinite and Solid Cohomology

Jiacheng Tang
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Abstract

Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having favourable categorical properties. Given a profinite ring $R$, there is an associated condensed ring $\underline{R}$ which is solid. We show that the natural embedding of profinite $R$-modules into solid $\underline{R}$-modules preserves $\mathrm{Ext}$ and tensor products, as well as the fact that profinite rings are analytic.

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Jiacheng Tang. 2024-10-11. Profinite and Solid Cohomology. https://arxiv.org/abs/2410.08933

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