Shifted Contact Structures and Their Local Theory

Berktav, Kadri İlker

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 33 (2024) no. 4, pp. 1019-1057

In this paper, we formally define $k$-shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for $k$-shifted contact derived $𝕂$-schemes, we develop a Darboux-like theorem and formulate the notion of symplectification.

Dans cet article, nous définissons formellement des structures contacts $k$-décalées sur des champs (d’Artin) dérivés et étudions leurs propriétés locales dans le contexte de la géométrie algébrique dérivée. À cet égard, pour les $𝕂$-schémas dérivés contacts $k$-décalés, nous développons un théorème de type Darboux et formulons la notion de symplectification.

Classification : 14A20, 14A30, 14F08
Keywords: derived algebraic geometry, shifted symplectic structures, contact geometry
Mots-clés : la géométrie algébrique dérivée, structures symplectiques décalées, géométrie contact

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