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We construct a quasi-coherent sheaf of associative algebras which controls acategory of $AV$-modules over a smooth quasi-projective variety. We establish alocal structure theorem, proving that in \'etale charts these associativealgebras decompose into a tensor product of the algebra of differentialoperators and the universal enveloping algebra of the Lie algebra of powerseries vector fields vanishing at the origin.

A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties