O-Minimality and Diophantine Geometry

doi:10.1017/CBO9781316106839

This collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre–Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila–Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
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 .

To save content items to your Kindle, first ensure no-reply@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.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Metrics

Altmetric attention score

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

O-Minimality and Diophantine Geometry

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Book description

Refine List

Actions for selected content:

Contents

Frontmatter
pp i-vi

Contents
pp vii-x

Preface
pp xi-xii

1 - The Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits
pp 1-40

2 - Rational points on definable sets
pp 41-65

3 - Functional transcendence via o-minimality
pp 66-99

4 - Introduction to abelian varieties and the Ax–Lindemann–Weierstrass theorem
pp 100-128

5 - The André-Oort conjecture via o-minimality
pp 129-158

6 - Lectures on elimination theory for semialgebraic and subanalytic sets
pp 159-192

7 - Relative Manin-Mumford for abelian varieties
pp 193-203

8 - Improving the bound in the Pila-Wilkie theorem for curves
pp 204-215

9 - Ax-Schanuel and o-minimality
pp 216-221

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

O-Minimality and Diophantine Geometry

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Altmetric attention score

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information