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Article Dans Une Revue Journal of the Institute of Mathematics of Jussieu Année : 2020

Derived Non-archimedean analytic Hilbert space

Jorge António
  • Fonction : Auteur
Mauro Porta

Résumé

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces.

Dates et versions

hal-02443392 , version 1 (17-01-2020)

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Jorge António, Mauro Porta. Derived Non-archimedean analytic Hilbert space. Journal of the Institute of Mathematics of Jussieu, 2020, ⟨10.1017/S1474748020000092⟩. ⟨hal-02443392⟩
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