Vol. 11, No. 5, 2017

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

Volume 14, 1 issue

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
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
Collinear CM-points

Yuri Bilu, Florian Luca and David Masser

Vol. 11 (2017), No. 5, 1047–1087

André’s celebrated theorem of 1998 implies that each complex straight line Ax + By + C = 0 (apart from obvious exceptions) contains at most finitely many points (j(τ),j(τ)), where τ,τ are algebraic of degree 2. We show that there are only a finite number of such lines which contain more than two such points. As there is a line through any two complex points, this is the best possible result.

CM points, André–Oort
Mathematical Subject Classification 2010
Primary: 11G15
Secondary: 11G18
Received: 2 January 2016
Revised: 27 November 2016
Accepted: 31 March 2017
Published: 12 July 2017
Yuri Bilu
Institut de Mathématiques de Bordeaux
Université de Bordeaux et CNRS
Florian Luca
School of Mathematics
University of the Witwatersrand
South Africa Max Planck Institute for Mathematics
David Masser
Mathematisches Institut
Universität Basel