Notes on acceptable bundles I

TL;DR

This paper studies acceptable bundles on a punctured disk within the Simpson--Mochizuki theory, introducing a new invariant and offering alternative arguments to existing proofs.

Contribution

It provides a detailed analysis of acceptable bundles, introduces a novel invariant, and presents new methods differing from prior work by Simpson and Mochizuki.

Findings

Introduction of a new invariant for acceptable bundles

Alternative arguments to existing proofs in the theory

Enhanced understanding of acceptable bundles on punctured disks

Abstract

The notion of acceptable bundles plays a fundamental role in the Simpson--Mochizuki theory. This paper presents a detailed study of acceptable bundles on a punctured disk. In addition to its expository aspects, we introduce a new invariant and provide arguments that differ from those of Simpson and Mochizuki.