A differential graded model for derived analytic geometry

Abstract

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.

24pp

References in corpus (6)

• Derived Algebraic Geometry V: Structured Spaces
• Homological Algebra for Superalgebras of Differentiable Functions
• Quantisation of derived Lagrangians
• Grothendieck topologies from unique factorisation systems
• Hyperskewness of $(1+1)$-dimensional KPZ Height Fluctuations
• The global derived period map