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arXiv · 1508.03007

The derived Maurer-Cartan locus

Ezra Getzler
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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 $L_+$.

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Ezra Getzler. 2016-03-23. The derived Maurer-Cartan locus. https://doi.org/10.4171/lem%2F62-1%2F2-14

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