CM-Points on Straight Lines

Abstract : We prove that, with "obvious" exceptions, a CM-point (j(\tau),j(\tau')) cannot belong to a straight line in C^2 defined over Q. This generalizes a result of K\"uhne, who proved this for the line x+y=1.
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https://hal.inria.fr/hal-01114121
Contributor : Karim Belabas <>
Submitted on : Saturday, February 7, 2015 - 3:54:45 PM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM

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Bill Allombert, Yuri Bilu, Amalia Pizarro-Madariaga. CM-Points on Straight Lines. Analytic Number Theory : In Honor of Helmut Maier’s 60th Birthday, 2015, 978-3-319-22239-4 ⟨10.1007/978-3-319-22240-0_1 ⟩. ⟨hal-01114121⟩

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