Skip to main content Accessibility help
×
Hostname: page-component-68945f75b7-9klrw Total loading time: 0 Render date: 2024-08-05T17:25:59.538Z Has data issue: false hasContentIssue false

11 - Variation of generic and subsidiary radii

from Part III - p-adic Differential Equations on Discs and Annuli

Published online by Cambridge University Press:  06 August 2022

Kiran S. Kedlaya
Affiliation:
University of California, San Diego
Get access

Summary

In this chapter, we apply the tools developed in the preceding chapters to study the variation of the generic radius of convergence and the subsidiary radii associated to a differential module on a disc or annulus. We have already seen some instances where this study is needed to deduce consequences about convergence of solutions of p-adic differential equations. The statements we formulate are modeled on statements governing the variation of the Newton polygon of a polynomial over a ring of power series, as we vary the choice of a Gauss norm on the power series ring. The guiding principle is that in the visible spectrum, one should be able to relate variation of subsidiary radii to variation of Newton polygons via matrices of action of the derivation on suitable bases. This includes the relationship between subsidiary radii and Newton polygons for cyclic vectors, but trying to use that approach directly creates no end of difficulties because cyclic vectors only exist in general for differential modules over fields. We implement the guiding principle in a somewhat more robust manner, using the work of Chapter 6 based on matrix inequalities.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×