On localizing topological algebras
Anastasios Mallios

TL;DR
This paper explores a class of topological algebras that generalize structure sheaf algebras using sheaf-theoretic localization, with potential applications in differential and algebraic geometry.
Contribution
It introduces geometric topological algebras based on Gel'fand transforms, highlighting their cohomological properties and stability under inductive limits.
Findings
Sheaf-theoretic localization underpins the structure of these algebras.
Geometric topological algebras possess special cohomological features.
The class of these algebras is closed under inductive limits.
Abstract
Through the subsequent discussion we consider a certain particular sort of (topological) algebras, which may substitute the `` structure sheaf algebras'' in many--in point of fact, in all--the situations of a geometrical character that occur, thus far, in several mathematical disciplines, as for instance, differential and/or algebraic geometry, complex (geometric) analysis etc. It is proved that at the basis of this type of algebras lies the sheaf-theoretic notion of (functional) localization, which, in the particular case of a given topological algebra, refers to the respective ``Gel'fand transform algebra'' over the spectrum of the initial algebra. As a result, one further considers the so-called ``geometric topological algebras'', having special cohomological properties, in terms of their ``Gel'fand sheaves'', being also of a particular significance for (abstract)…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Topics in Algebra
