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arXiv · 1906.07044

Derived Non-archimedean analytic Hilbert space

Jorge António·Mauro Porta
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Abstract

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.

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Jorge António, Mauro Porta. 2019-06-17. Derived Non-archimedean analytic Hilbert space. https://doi.org/10.1017/s1474748020000092

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