Topologization and Functional Analytification I: Intrinsic Morphisms of Commutative Algebras

Abstract

Eventually after Dieudonné-Grothendieck, we give intrinsic definitions of étale, lisse and non-ramifié morphisms for general adic rings and general locally convex rings. And we investigate the corresponding étale-like, lisse-like and non-ramifié-like morphisms for general $\infty$-Banach, $\infty$-Borné and $\infty$-ind-Fréchet $\infty$-rings and $\infty$-functors into $\infty$-groupoid (as in the work of Bambozzi-Ben-Bassat-Kremnizer) in some intrinsic way by using the corresponding infinitesimal stacks and crystalline stacks. The two directions of generalization will intersect at Huber's book in the strongly noetherian situation.

34 pages

References in corpus (1)

• p-adic derived de Rham cohomology