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arXiv · 1303.4941

Un sch\'ema simplicial de Grothendieck-Pridham

Brahim Benzeghli
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Abstract

Pridham has shown that any Artin $n$-stack $M$ has a presentation as a simplicial scheme $X$ satisfying certain smoothness properties originally introduced by Grothendieck. In the previous paper we introduced an Artin $n$-stack $M$ of Maurer-Cartan elements of a dg-category and constructed a chart, and have already proven the first conditions of smoothness of $X_1\rightarrow X_0$ explicitly. In this paper, we will construct explicitly the full simplicial scheme and show the Grothendieck-Pridham smoothness conditions, implying that $M$ is a geometric $n$-stack.

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Brahim Benzeghli. 2013-03-20. Un sch\'ema simplicial de Grothendieck-Pridham. https://arxiv.org/abs/1303.4941

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