论文标题
$ \ wideHat {\ mathcal {d}}}^{（0）} _ {\ Mathfrak {x}，k，k，\ mathbb {q}} $ - 模块
$\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k, \mathbb{Q}}$-modules holonomes sur une courbe formelle
论文作者
论文摘要
让$ \ mathfrak {x} $成为完整的离散评估环$ \ Mathcal {V} $的正式平滑曲线，混合特性$（0，p）$。令$ \ wideHat {\ mathcal {d}}}^{（0）} _ {\ Mathfrak {x}，\ Mathbb {q}} $是级别0级别的差异差异操作员的捆，即导数产生）。在这种情况下，Garnier证明了自动$ \ wideHat {\ Mathcal {d}}}^{（0）} _ {\ Mathfrak {\ Mathfrak {X}，\ Mathbb {q}} $ - 由Berthelot定义的模块，由Berthelot定义为有限长度。在本文中，我们将此问题用于$ \ wideHat {\ Mathcal {d}}}^{（0）} _ {\ Mathfrak {\ Mathfrak {X}，K，\ Mathbb {Q}} $ Qualte late $ k $ k $ k $ j $ j $ j $ j $定义的Christine huyghe huyghe huyghe，tobias schmias schmidt and Matthias and the and。使用与Garnier相同的策略，我们证明了自变量$ \ wideHat {\ Mathcal {d}}}}^{（0）} _ {\ Mathfrak {X}，k，k，\ mathbb {q}} $ - 模块具有有限的长度。最终，我们通过证明与曲线上具有集成连接的可共同模块具有有限的长度，从而对可辅助模块进行了应用。
Let $\mathfrak{X}$ be a formal smooth curve over a complete discrete valuation ring $\mathcal{V}$ of mixed characteristic $(0 , p)$. Let $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, \mathbb{Q}}$ be the sheaf of crystalline differential operators of level 0 (i.e., generated by the derivations). In this situation, Garnier proved that holonomic $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, \mathbb{Q}}$-modules as defined by Berthelot have finite length. In this article, we address this question for the sheaves $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k , \mathbb{Q}}$ of congruence level $k$ defined by Christine Huyghe, Tobias Schmidt and Matthias Strauch. Using the same strategy as Garnier, we prove that holonomic $\widehat{\mathcal{D}}^{(0)}_{\mathfrak{X}, k , \mathbb{Q}}$-modules have finite length. We finally give an application to coadmissible modules by proving that coadmissible modules with integrable connection over curves have finite length.
