Topological sheaves and spaces of distributions in the global case

2025/01/15 by Luca Casarin, Casarin, Luca, Andrea Maffei +1
Mathematics · #17B65 #17B69 #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical and Theoretical Analysis #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2501.08935

openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their basic properties. We then construct appropriate analogues of the spaces of fields, consider multiplication of fields between them and rebuild the basic theory of vertex algebras in the setting of global distributions in place of formal power series, which takes the form of chiral algebras introduced Beilinson and Drinfeld in "Chiral Algebras".

Related

• Brief Notes on Sheaves Theory
• Distributions with locally free tangent sheaf
• Generalised subbundles and distributions: A comprehensive review
• A note on exponential varieties, statistical manifolds and Frobenius\n structures
• Sheaves and K-theory for \mathbbF₁-schemes