Annihilators of AV-modules and differential operators

2022/11/16 by Emile Bouaziz, Bouaziz, Emile, Henrique Rocha +1
Computer Science · Mathematics · #17B10 #17B66 #32C38 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2211.09211

openalex publication_date 2022/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a smooth algebraic variety X, we study the category of finitely generated modules over the ring of function of X that has a compatible action of the Lie algebra V of polynomials vector fields on X. We show that the associated representation of V is given by a differential operator of order depending on the rank of the module. The order of the differential operator provides a natural measure of the complexity of the representation, with the simplest case being that of D-modules.

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