Vol. 14, No. 6, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Uniform Yomdin–Gromov parametrizations and points of bounded height in valued fields

Raf Cluckers, Arthur Forey and François Loeser

Vol. 14 (2020), No. 6, 1423–1456

We prove a uniform version of non-Archimedean Yomdin–Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of 𝔽q[t]-points of bounded degrees of algebraic varieties, uniformly in the cardinality q of the finite field 𝔽q and the degree, generalizing work by Sedunova for fixed q. We also deduce a uniform non-Archimedean Pila–Wilkie theorem, generalizing work by Cluckers–Comte–Loeser.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

rational points, points of bounded height, parametrizations
Mathematical Subject Classification 2010
Primary: 14G05
Secondary: 03C98, 11D88, 11G50
Received: 18 February 2019
Revised: 9 January 2020
Accepted: 3 March 2020
Published: 30 July 2020
Raf Cluckers
University of Lille
CNRS, UMR 8524 – Laboratoire Paul Painlevé
F-59000 Lille
KU Leuven
Department of Mathematics
Arthur Forey
ETH Zürich
François Loeser
Institut Universitaire de France
Sorbonne Université
Institut Mathématique de Jussieu