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arXiv · 2302.07918

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

Yuly Billig·Colin Ingalls
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Abstract

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

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Yuly Billig, Colin Ingalls. 2023-02-15. A universal sheaf of algebras governing representations of vector fields on quasi-projective varieties. https://arxiv.org/abs/2302.07918

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