Profinite and solid cohomology

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 $\underset{\_}{R}$ which is solid. We show that the natural embedding of profinite R-modules into solid $\underset{\_}{R}$-modules preserves Ext and tensor products, as well as the fact that profinite rings are analytic.