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arXiv · 2111.01735

Cohomology of Lie algebroids over algebraic spaces

Abhishek Sarkar
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Abstract

We consider Lie algebroids over an algebraic space (or topological ringed space) as quasicoherent sheaves of Lie-Rinehart algebras. We express hypercohomology for a locally free Lie algebroid (not necessarily of finite rank) as a derived functor, and simplify it via \v{C}ech cohomology. Furthermore, we define the Hochschild hypercohomology of a sheaf of generalized bialgebras and study the cases of the universal enveloping algebroid and the jet algebroid of a Lie algebroid. In the sequel, we present a version of Hochschild-Kostant-Rosenberg theorem for a locally free Lie algebroid, as well as its dual version.

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Abhishek Sarkar. 2021-11-02. Cohomology of Lie algebroids over algebraic spaces. https://arxiv.org/abs/2111.01735

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