Affiliation:
1. Dipartimento di Matematica University of Padova Padova Italy
2. Mathematical Institute University of Oxford Oxford UK
Abstract
AbstractLet be a non‐Archimedean Banach ring, satisfying some mild technical hypothesis that we will specify later on. We prove that it is possible to associate to a homotopical Huber spectrum via the introduction of the notion of derived rational localization. The spectrum so obtained is endowed with a derived structural sheaf of simplicial Banach algebras for which the derived C̆ech–Tate complex is strictly exact. Under some hypothesis, we can prove that there is a canonical morphism of underlying topological spaces that is a homeomorphism in some well‐known examples of non‐sheafy Banach rings, where is the usual Huber spectrum of . This permits the use of the tools from derived geometry to understand the geometry of in cases when the classical structure sheaf is not a sheaf.
Funder
Deutsche Forschungsgemeinschaft
Reference26 articles.
1. F.Bambozzi On a generalization of affinoid varieties Ph.D. thesis University of Padova 2013.
2. Dagger geometry as Banach algebraic geometry
3. Stein domains in Banach algebraic geometry
4. Analytic geometry over F1 and the Fargues-Fontaine curve
5. F.BambozziandK.Kremnizer Relations between bornological and condensed structures—algebraic theory in progress.