Derived deformation functors, Koszul duality, and Maurer-Cartan spaces
Algebraic Geometry
2025-08-08 v2 Algebraic Topology
Quantum Algebra
Abstract
We summarise the chain of comparisons showing Hinich's derived Maurer-Cartan functor gives an equivalence between differential graded Lie algebras and derived Schlessinger functors on Artinian differential graded-commutative algebras. We include some motivating deformation problems and analogues for more general Koszul dual pairs of operads.
Keywords
Cite
@article{arxiv.2503.05307,
title = {Derived deformation functors, Koszul duality, and Maurer-Cartan spaces},
author = {J. P. Pridham},
journal= {arXiv preprint arXiv:2503.05307},
year = {2025}
}
Comments
16pp., survey with some new material; v2 final version, to appear in Philosophical Transactions of the Royal Society A