Slope filtrations revisited

TL;DR

This paper offers a refined and simplified exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, highlighting analogies with stable vector bundles.

Contribution

It provides a second-generation, simplified proof of the slope filtration theorem, inspired by parallel work and analogies with stable vector bundles.

Findings

Simplified the proof of the slope filtration theorem.

Draws parallels between Frobenius modules and stable vector bundles.

Highlights conceptual analogies enhancing understanding.

Abstract

We give a "second generation" exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.