标题： 算术$\mathscr{D}$模的刚化与超收敛黎曼-希尔伯特对应关系 显示英文标题

标题： Rigidification of arithmetic $\mathscr{D}$-modules and an overconvergent Riemann-Hilbert correspondence

摘要： 在本文中，我定义了在正特征的完美域上的代数簇上构造性等距晶体的三角范畴，在其中Le Stum的构造性等距晶体的阿贝尔范畴是自然t-结构的中心。 然后我证明了一个黎曼-希尔伯特对应关系，表明对于某些（未指定）弗罗贝尼乌斯结构的对象，这个三角范畴与Caro所定义的超全纯$\mathscr{D}^\dagger$-模的三角范畴等价。 我还证明了为$\mathscr{D}^\dagger$-模定义的上同调函子$f^!$、$f_+$和$\otimes$在这个对应关系的构造性方面有自然的解释。 最后，我利用这一点证明了，对于任何能够浸入到光滑且完备的形式概形中的代数簇$X$，刚性上同调（带有有限系数）与使用算术$\mathscr{D}$-模定义的上同调一致。 显示英文摘要

摘要： In this article, I define triangulated categories of constructible isocrystals on varieties over a perfect field of positive characteristic, in which Le Stum's abelian category of constructible isocrystals sits as the heart of a natural t-structure. I then prove a Riemann-Hilbert correspondence, showing that, for objects admitting some (unspecified) Frobenius, this triangulated category is equivalent to the triangulated category of overholonomic $\mathscr{D}^\dagger$-modules in the sense of Caro. I also show that the cohomological functors $f^!$, $f_+$ and $\otimes$ defined for $\mathscr{D}^\dagger$-modules have natural interpretations on the constructible side of this correspondence. Finally, I use this to prove that, for any variety $X$ admitting an immersion into a smooth and proper formal scheme, rigid cohomology (with lisse coefficients) agrees with cohomology defined using arithmetic $\mathscr{D}$-modules.