Differential modules on p-adic polyannuli

TL;DR

This paper studies the behavior of numerical invariants related to differential modules on p-adic polyannuli, extending previous one-dimensional results and applicable to complex manifolds and isocrystals.

Contribution

It generalizes the variational analysis of convergence invariants for differential modules from one-dimensional cases to higher-dimensional polyannuli over nonarchimedean fields.

Findings

Extended variational properties to higher dimensions

Applicable to nonarchimedean fields of characteristic zero

Relevance to Swan conductors and complex manifold connections

Abstract

We consider variational properties of some numerical invariants, measuring convergence of local horizontal sections, associated to differential modules on polyannuli over a nonarchimedean field of characteristic zero. This extends prior work in the one-dimensional case of Christol, Dwork, Robba, Young, et al. Our results do not require positive residue characteristic; thus besides their relevance to the study of Swan conductors for isocrystals, they are germane to the formal classification of flat meromorphic connections on complex manifolds.