Microlocalisation d'opérateurs différentiels arithmétiques sur un schéma formel lisse - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

Microlocalisation d'opérateurs différentiels arithmétiques sur un schéma formel lisse

Abstract

Let $\mathfrak{X}$ be a formal smooth quasi-compact scheme over a complete discrete valuation ring $\mathcal{V}$ of mixed characteristic $(0 , p)$. We consider the sheaves of differential operators $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k , \mathbb{Q}}$ with a congruence level $k \in \mathbb{N}$ and their projective limit $\mathcal{D}_{\mathfrak{X}, \infty} = \varprojlim_k \widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k , \mathbb{Q}}$. In this article, we construct microlocalization sheaves of $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k , \mathbb{Q}}$ for the different congruence levels $k$ admitting transition morphisms. Then we pass to the projective limit over $k$ in order to obtain some microlocalization sheaves of $\mathcal{D}_{\mathfrak{X}, \infty}$. These sheaves will be useful later to define a characteristic variety for coadmissible $\mathcal{D}_{\mathfrak{X}, \infty}$-modules when $\mathfrak{X}$ is a formal curve.
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Dates and versions

hal-03975658 , version 1 (07-02-2023)
hal-03975658 , version 2 (12-05-2023)
hal-03975658 , version 3 (02-08-2023)
hal-03975658 , version 4 (12-01-2024)
hal-03975658 , version 5 (25-01-2024)

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Cite

Raoul Hallopeau. Microlocalisation d'opérateurs différentiels arithmétiques sur un schéma formel lisse. 2024. ⟨hal-03975658v5⟩
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