Séminaire Géométrie et Quantification

Koszul Duality for Lie Algebroids

by Prof. Joost-Jakob Nuiten (Montpellier)

Centre de conférences Marilyn et James Simons (IHES)

Centre de conférences Marilyn et James Simons



A classical principle in deformation theory asserts that any formal deformation problem over a field of characteristic zero is classified by a differential graded Lie algebra. Using the Koszul duality between Lie algebras and commutative algebras, Lurie and Pridham have given a more precise description of this principle: they establish an equivalence of categories between dg-Lie algebras and formal moduli problems indexed by Artin commutative dg-algebras. I will describe a variant of this result for deformation problems around schemes over a field of characteristic zero. In this case, there is an equivalence between the homotopy categories of dg-Lie algebroids and formal moduli problems on a derived scheme. This can be viewed as a derived version of the relation between Lie algebroids and formal groupoids.

Organized by

Anton Alekseev (Univ. Genève), Pierre Cartier (IHES),Yvette Kosmann-Schwarzbach (Paris), Volodya Roubstov (Univ. d’Angers), Camille Laurent-Gengoux (Lorraine)