Analytic Geometry and Hodge-Frobenius Structure Continued

TL;DR

This paper extends previous work on generalized Frobenius modules over multivariate Robba rings, exploring analytic functions on polydiscs and polyannuli, and examining admissible Hodge-Frobenius structures in a broader context.

Contribution

It advances the theory of Hodge-Frobenius structures by generalizing to multivariate Robba rings and analyzing their analytic and admissibility properties.

Findings

Extended the framework of Frobenius modules to multivariate settings

Analyzed analytic functions on polydiscs and polyannuli in this context

Identified conditions for admissibility of Hodge-Frobenius structures

Abstract

This is our sequel to our previous work on the corresponding generalized Frobenius modules over some big multivariate Robba rings. We will go beyond our previous discussion where we focused on the corresponding analytic functions on polydiscs and polyannuli in the strictly affinoid situation, and general Hodge-Frobenius structures which are admissible in the corresponding context in our previous work.