∞-Categorical Perverse p-adic Differential Equations over Stacks
Abstract
We will discuss ∞-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 \'etale fundamental groups in the \'etale 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-Z\'abr\'adi and Pal-Z\'abr\'adi. On the other hand, we are going to establish the ∞-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.