论文标题
$ \ infty $ - 类别不正当$ p $ - adic微分方程堆栈
$\infty$-Categorical Perverse $p$-adic Differential Equations over Stacks
论文作者
论文摘要
我们将讨论$ \ infty $ - 分类差异$ p $ - adic微分方程。一方面，我们将在Kedlaya和Kedlaya-XU之后紧密地研究了Drinfeld的原始引理的一些$ P $ - 采用类似结果。我们期望在Scholze之后的钻石中也可以考虑类似的事情，在Kedlaya-Liu的作品中，即伪造的Frobenius Sheaves的派生类别，这将引起Drinfeld的Lemma的某种类别形式，用于Carter-Kedlaya-kedlaya-kedlaya-Zábrádi和pal-z的钻石。另一方面，我们将建立Abe和GaitSgory-Lurie之后的$ \ Infty $分类理论，该理论将允许一个人构建刚性的总$ g $ - 动物。而且我们希望将整个机械应用于韦尔的猜想，并在步态策略之后平行和之后。
We will discuss $\infty$-categorical perverse $p$-adic differential equations over stacks. On one hand, we are going to study some $p$-adic analogous results of the Drinfeld's original lemma about the étale fundamental groups in the étale setting, in the context of $F$-isocrystals closely after Kedlaya and Kedlaya-Xu. We expect similar things could also be considered for diamonds after Scholze, in the context of Kedlaya-Liu's work namely the derived category of pseudocoherent Frobenius sheaves, which will induce some categorical form of Drinfeld's lemma for diamonds motivated by work of Carter-Kedlaya-Zábrádi and Pal-Zábrádi. On the other hand, we are going to establish the $\infty$-categorical theory of arithmetic $D$-modules after Abe and Gaitsgory-Lurie, which will allow one to construct the rigid Gross $G$-motives. And we are expecting to apply the whole machinery to revisit Weil's conjecture parallel to and after Gaitsgory-Lurie.
