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2017 Collinear CM-points
Yuri Bilu, Florian Luca, David Masser
Algebra Number Theory 11(5): 1047-1087 (2017). DOI: 10.2140/ant.2017.11.1047

Abstract

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.

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Yuri Bilu. Florian Luca. David Masser. "Collinear CM-points." Algebra Number Theory 11 (5) 1047 - 1087, 2017. https://doi.org/10.2140/ant.2017.11.1047

Information

Received: 2 January 2016; Revised: 27 November 2016; Accepted: 31 March 2017; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06748166
MathSciNet: MR3671431
Digital Object Identifier: 10.2140/ant.2017.11.1047

Subjects:
Primary: 11G15
Secondary: 11G18

Keywords: André–Oort , CM points

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2017
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