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Keywords:
derived algebraic geometry; shifted symplectic structures; contact geometry
derived algebraic geometry; shifted symplectic structures; contact geometry
Summary:
This is a sequel of [2] on the development of derived contact geometry. In [2], we formally introduced shifted contact structures on derived stacks. We then gave a Darboux-type theorem and the notion of symplectification only for negatively shifted contact derived schemes. In this paper, we extend the results of [2] from derived schemes to derived Artin stacks and provide some examples of contact derived Artin stacks. In brief, we first show that for $k < 0$, every $k$-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a $k$-shifted contact structure, where $k < 0$. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures.
References:
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