G\'eom\'etricit\'e artinienne de l'$\mathrm{\infty }$-champs des \'el\'ements de Maurer-Cartan

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 $\mathrm{\infty }$-stack $Perf$, we explicitly construct a new Artin $\mathrm{\infty }$-stack of Maurer-Cartan elements of a dg-category $ \mathcal {P} $denotedby$$\mathcal{M}{\mathcal{C}}_{\mathcal{P}}$ $,withamap$ V \to $\mathcal{M}{\mathcal{C}}_{\mathcal{P}}$ $ which we show to be formally smooth.