Mathematics > Number Theory
[Submitted on 13 Jan 2022 (v1), last revised 20 Jan 2022 (this version, v2)]
Title:$\infty$-Categorical Perverse $p$-adic Differential Equations over Stacks
View PDFAbstract: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.
Submission history
From: Xin Tong [view email][v1] Thu, 13 Jan 2022 14:35:16 UTC (18 KB)
[v2] Thu, 20 Jan 2022 15:08:29 UTC (20 KB)
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