论文标题
代数叶子和衍生几何形状：Riemann-Hilbert对应关系
Algebraic foliations and derived geometry: the Riemann-Hilbert correspondence
论文作者
论文摘要
这是一系列有关衍生几何形状叶子的论文中的第一篇。在对任意派生的堆栈引入了衍生的叶子后，我们集中于准平滑和刚性衍生的叶子，这些叶子在光滑的复杂代数品种及其相关的形式和分析版本上。他们的截断是古典的奇异叶子。我们证明，在光滑的复杂品种上的准平滑刚性衍生的叶片$ x $在任何时候都是正式集成的，如果我们假设其奇异基因座具有编纂$ \ geq 2 $，那么其分析化的截断是在相关的复杂复合物$ x^h $ x^h $ x^h $上的本地集成的单数叶面。然后，我们在$ x $上的准平滑刚性衍生的叶片上介绍了完美晶体的派生类别，并在$ x $适当时证明了他们的riemann-hilbert通信。我们讨论了几个示例和应用程序。
This is the first in a series of papers about foliations in derived geometry. After introducing derived foliations on arbitrary derived stacks, we concentrate on quasi-smooth and rigid derived foliations on smooth complex algebraic varieties and on their associated formal and analytic versions. Their truncations are classical singular foliations. We prove that a quasi-smooth rigid derived foliation on a smooth complex variety $X$ is formally integrable at any point, and, if we suppose that its singular locus has codimension $\geq 2$, then the truncation of its analytification is a locally integrable singular foliation on the associated complex manifold $X^h$. We then introduce the derived category of perfect crystals on a quasi-smooth rigid derived foliation on $X$, and prove a Riemann-Hilbert correspondence for them when $X$ is proper. We discuss several examples and applications.
