Algebraic geometry in tensor categories

2023/11/03 by Kevin Coulembier, Coulembier, Kevin
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.02264

openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We set up some foundations of generalised scheme theory related to new incompressible symmetric tensor categories. This is analogous to the relation between super schemes and the category of super vector spaces.

Related

• Commutative algebra in tensor categories
• Group schemes and their Lie algebras over a symmetric tensor category
• Tensor Operations on Group Schemes
• Tensor categorical foundations of algebraic geometry
• Inductive systems of the symmetric group, polynomial functors and tensor categories