The derived Maurer-Cartan locus

Abstract

The derived Maurer-Cartan locus ${\text{MC}}^{\bullet }(L)$ is a functor from differential graded Lie algebras to cosimplicial schemes. If L is differential graded Lie algebra, let $L_{+}$ be the truncation of $L$ in positive degrees $i>0$. We prove that the differential graded algebra of functions on the cosimplicial scheme ${\text{MC}}^{\bullet }(L)$ is quasi-isomorphic to the Chevalley-Eilenberg complex of $L_{+}$.

18 pages; final version, to appear in L'Enseignement Mathématique; formulas for codegeneracy and coface maps in derived Maurer-Cartan locus are corrected from first version; introduction now includes several examples of derived Maurer-Cartan loci and derived Deligne-Mumford groupoids

Cited by in corpus (1)

• The Hodge Chern character of holomorphic connections as a map of simplicial presheaves