Differentiable holonomic AV-modules

2025/11/18 by Billig, Yuly, Rocha, Henrique
Mathematics · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory

paper · doi:10.48550/arxiv.2511.14984

Abstract

We study differentiable holonomic sheaves of AV-modules on a smooth quasi-projective variety. We show that a simple differentiable holonomic sheaf M of AV-modules is locally the tensor product of a simple holonomic D-module and a simple finite-dimensional gl_n-module W. In particular, in the case when W is integrable, M is the tensor product of a simple holonomic D-module and the tensor module associated with W.

Citations

• Sheaves of AV-modules on quasi-projective varieties
• A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties
• Classification of simple bounded weight modules of the Lie algebra of vector fields on \Cⁿ
• Gauge modules for the Lie algebras of vector fields on affine varieties
• Representations of Lie algebras of vector fields on affine varieties
• Lie algebras of vector fields on smooth affine varieties

Related

• Holonomic AV-modules for the affine space
• Holonomic D-modules on abelian varieties
• Three results on holonomic D-modules
• Holonomic étale sheaves are constructible
• Regularization of relative holonomic D-modules