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Theses

Derived integral models and its applications to the study of certain derived rigid analytic moduli spaces

Abstract : In this thesis, we study different aspects of derived k-analytic geometry. Namely, we extend the theory of classical formal models for rigid k-analytic spaces to the derived setting. Having a theory of derived formal models at our disposal we proceed to study certain applications such as the representability of derived Hilbert stack in the derived k-analytic setting. We construct a moduli stack of derived k-adic representations of profinite spaces and prove its geometricity as a derived k-analytic stack. Under certain hypothesis we show the existence of a natural shifted symplectic structure on it. Our main applications is to study pro-étale k-adic local systems on smooth schemes in positive characteristic. Finally, we study at length an analytic analogue (both over the field of complex numbers C and over a non-archimedean field k) of the structured algebraic HKR, proved by Toen and Vezzosi.
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Jorge Ferreira Antonio. Derived integral models and its applications to the study of certain derived rigid analytic moduli spaces. Algebraic Geometry [math.AG]. Université Paul Sabatier - Toulouse III, 2019. English. ⟨NNT : 2019TOU30040⟩. ⟨tel-02893895⟩

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