On the torsion anomalous conjecture in CM abelian varieties

Sara Checcoli and Evelina Viada

Vol. 271 (2014), No. 2, 321–345

DOI: 10.2140/pjm.2014.271.321

Abstract

The torsion anomalous conjecture (TAC) states that a subvariety $V$ of an abelian variety $A$ has only finitely many maximal torsion anomalous subvarieties. In this work we prove, with an effective method, some cases of the TAC when the ambient variety $A$ has CM, generalising our previous results in products of CM elliptic curves. When $V$ is a curve, we give new results and we deduce some implications on the effective Mordell–Lang conjecture.

Keywords

diophantine approximation, heights, abelian varieties, intersections with torsion varieties

Mathematical Subject Classification 2010

Primary: 11G50

Secondary: 14G40

Milestones

Received: 10 July 2013

Revised: 6 May 2014

Accepted: 10 May 2014

Published: 20 September 2014