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- W1945812824 abstract "To any non-negatively graded dg Lie algebra $g$ over a field $k$ of characteristic zero we assign a functor $Sigma_g: art/k to Kan$ from the category of commutative local artinian $k$-algebras with the residue field $k$ to the category of Kan simplicial sets. There is a natural homotopy equivalence between $Sigma_g$ and the Deligne groupoid corresponding to $g$. The main result of the paper claims that the functor $Sigma$ commutes up to homotopy with the total functors which assign a dg Lie algebra to a cosimplicial dg Lie algebra and a simplicial set to a cosimplicial simplicial set. This proves a conjecture of Schechtman which implies that if a deformation problem is described ``locally'' by a sheaf of dg Lie algebras $g$ on a topological space $X$ then the global deformation problem is described by the homotopy Lie algebra $RGamma(X,g)$." @default.
- W1945812824 created "2016-06-24" @default.
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- W1945812824 date "1996-06-11" @default.
- W1945812824 modified "2023-09-27" @default.
- W1945812824 title "Descent of Deligne groupoids" @default.
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