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arXiv · 1712.03442

Koszul duality for Lie algebroids

Joost Nuiten
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Abstract

This paper studies the role of dg-Lie algebroids in derived deformation theory. More precisely, we provide an equivalence between the homotopy theories of formal moduli problems and dg-Lie algebroids over a commutative dg-algebra of characteristic zero. At the level of linear objects, we show that the category of representations of a dg-Lie algebroid is an extension of the category of quasi-coherent sheaves on the corresponding formal moduli problem. We describe this extension geometrically in terms of pro-coherent sheaves.

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Joost Nuiten. 2017-12-09. Koszul duality for Lie algebroids. https://arxiv.org/abs/1712.03442

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