Hodge-Iwasawa Theory II

TL;DR

This paper advances Hodge-Iwasawa theory by exploring higher-dimensional deformations of Hodge structures over analytic spaces, utilizing Frobenius modules and period rings, aiming to develop foundational tools for moduli of Frobenius sheaves.

Contribution

It extends previous work on Hodge-Iwasawa theory by generalizing period rings and studying their sheaf-theoretic organization for applications to Frobenius sheaves moduli.

Findings

Generalized perfect and imperfect period rings.

Framework for globalizing deformed period rings.

Foundations for moduli of Frobenius sheaves.

Abstract

We continue our study on the Hodge-Iwasawa theory which is a continuation of our previous work on Hodge-Iwasawa theory, which is aimed at higher dimensional deformation of higher dimensional Hodge structures over general analytic spaces or adic spaces. We still follow closely the approaches of Kedlaya-Liu to study our Frobenius modules over the different kinds of period rings including more generalized perfect period rings and the corresponding imperfect period rings. It is desirable that one can globalize the deformed information in order to organize the deformed period rings into the corresponding sheaves with respect to the coefficient sheaves, which will build up some foundations on further application to moduli of Frobenius sheaves.