Maurer-Cartan spaces of filtered L-infinity algebras

2014/09/16 by Yalin, Sinan
#Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1409.4741

Abstract

We study several homotopical and geometric properties of Maurer-Cartan spaces for L-infinity algebras which are not nilpotent, but only filtered in a suitable way. Such algebras play a key role especially in the deformation theory of algebraic structures. In particular, we prove that the Maurer-Cartan simplicial set preserves fibrations and quasi-isomorphisms. Then we present an algebraic geometry viewpoint on Maurer-Cartan moduli sets, and we compute the tangent complex of the associated algebraic stack.

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