A differential graded model for derived analytic geometry

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We give a formulation for derived analytic geometry built from commutative differential graded algebras equipped with entire functional calculus on their degree 0 part, a theory well-suited to developing shifted Poisson structures and quantisations. In the complex setting, we show that this formulation recovers equivalent derived analytic spaces and stacks to those coming from Lurie's structured topoi. In non-Archimedean settings, there is a similar comparison, but for derived dagger analytic spaces and stacks, based on overconvergent functions.
Original languageEnglish
Number of pages24
JournalAdvances in Mathematics
Early online date26 Nov 2019
Publication statusPublished - 22 Jan 2020


  • math.AG


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