Comparison between formal slopes and p-adic slopes

TL;DR

This paper compares formal slopes and p-adic slopes of solvable differential modules over the punctured open unit disc, using Newton polygons and the log-convexity of generic radius functions to establish inequalities.

Contribution

It introduces new inequalities relating formal and p-adic slopes, advancing understanding of differential modules in p-adic analysis.

Findings

Established inequalities between formal and p-adic slopes.

Analyzed Newton polygons and radius functions for differential modules.

Provided insights into the structure of solvable differential modules.

Abstract

In this paper, we establish several inequalities comparing formal slopes with p-adic slopes of solvable differential modules over the punctured open unit disc. Our approach is based on a delicate analysis of Newton polygons and the log-convexity of generic radius functions.