Géométricité artinienne de l'$\infty$-champs des éléments de Maurer-Cartan

Abstract

In this paper, based on the same techniques as in \cite{BENZ08} for the construction of a formally smooth map $V\to Perf$ from the variety of complexes to the Artin $\infty$-stack $Perf$, we explicitly construct a new Artin $\infty$-stack of Maurer-Cartan elements of a dg-category $\mathcal{P}$ denoted by $\mathcal{M}{\mathcal{C}}_{\mathcal{P}}$, with a map $V\to \mathcal{M}{\mathcal{C}}_{\mathcal{P}}$ which we show to be formally smooth.

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• Non-commutative derived moduli prestacks