$\infty$-Categorical Approaches to Hodge-Iwasawa Theory II: $\infty$-Categorical and Derived Hodge-Iwasawa Modules

Xin Tong

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arXiv · 2311.10022

$\infty$-Categorical Approaches to Hodge-Iwasawa Theory II: $\infty$-Categorical and Derived Hodge-Iwasawa Modules

Xin Tong

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Abstract

This paper is a discussion on $\infty$-categorical approaches to Hodge-Iwasawa Theory, which was initiated in our project on the $\infty$-categorical approaches to Hodge-Iwasawa Theory. The theory aims at the serious unification of $p$-adic Hodge Theory and $p$-adic Iwasawa Theory, by taking deformation of Hodge-theoretic constructions along some consideration in Iwasawa Theory beyond the Iwasawa deformation of certain motives in the general sense. The Hodge modules in our current consideration will be essentially within $\infty$-categorical derived categories of inductive Banach modules and $\infty$-categorical derived categories of condensed solidification of certain topological modules.

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Xin Tong. 2023-11-16. $\infty$-Categorical Approaches to Hodge-Iwasawa Theory II: $\infty$-Categorical and Derived Hodge-Iwasawa Modules. https://arxiv.org/abs/2311.10022

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