$\infty$-Categorical Approaches to Hodge-Iwasawa Theory I: Introduction and Extensions

Abstract

In this paper, we give the introduction to the Hodge-Iwasawa Theory introduced by the author. After that we will give some well-defined extensions to the already shaped framework established in our previous work.

169 pages. Based on our dissertation on the title of the Geometric and Representation Theoretic Aspects of p-adic Motives. Added the corresponding Clausen-Scholze formalism on solid quasicoherent sheaves, solid vector bundles and solid perfect complexes, as well as liquid quasicoherent sheaves, liquid vector bundles and liquid perfect complexes