论文标题
紧凑型刚性和$ \ pmb {\ mathscr {d}} $之间的比较
A comparison between compactly supported rigid and $\pmb{\mathscr{D}}$-module cohomology
论文作者
论文摘要
本文的目的是证明使用算术理论$ \ Mathscr {d} $ - 模块计算出的刚性共同体学和共同体之间的比较定理。为此，我们从LE Stum的构造等级晶体类别构建了一个专业函数到算术$ \ Mathscr {d} $ - 模块的派生类别。对于“ Frobenius类型”的对象，我们表明该函子的基本图像由过度的$ \ Mathscr {d}^\ Dagger $ -Modules组成，并且位于双重构造t结构的心脏内部。我们使用它为Caro的专业化函数$ \ mathrm {sp} _+$提供了更全球化的构造，用于过度融合的等法晶体，这使我们能够证明对紧凑型支持的共同体的比较定理。
The goal of this article is to prove a comparison theorem between rigid cohomology and cohomology computed using the theory of arithmetic $\mathscr{D}$-modules. To do this, we construct a specialisation functor from Le Stum's category of constructible isocrystals to the derived category of arithmetic $\mathscr{D}$-modules. For objects `of Frobenius type', we show that the essential image of this functor consists of overholonomic $\mathscr{D}^\dagger$-modules, and lies inside the heart of the dual constructible t-structure. We use this to give a more global construction of Caro's specialisation functor $\mathrm{sp}_+$ for overconvergent isocrystals, which enables us to prove the comparison theorem for compactly supported cohomology.
