Sheaves of AV-modules over projective varieties

Abstract: AV-modules are representations of the Lie algebra $V$ of vector fields that admit a compatible action of the commutative algebra $A$ of functions. This notion is a natural generalization of $\mathcal D$-modules. In this talk we shall start by reviewing the theory of AV-modules over smooth irreducible affine varieties $X$. When the variety $X$ is projective, it is necessary to consider sheaves of AV-modules. We describe associative algebras that control the category of AV-modules, and construct a functor from the category of strong representations of Lie algebra of jets of vector fields to the category of AV-modules. This talk is based on the joint work with Colin Ingalls, as well as the work of Emile Bouaziz and Henrique Rocha.

mathematical physicscommutative algebraalgebraic geometrycategory theorydifferential geometryrings and algebrasrepresentation theory

Audience: researchers in the topic

Comments: Hybrid delivery (in person on University of Saskatchewan campus and via Zoom).

PIMS Geometry / Algebra / Physics (GAP) Seminar