Problème de Mordell-Lang modulo certaines sous-variétés abéliennes

Rémond, Gaël and Viada, Evelina. (2003) Problème de Mordell-Lang modulo certaines sous-variétés abéliennes. International Mathematics Research Notices, 2003 (35). pp. 1915-1931.

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Official URL: http://edoc.unibas.ch/dok/A5260091

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Following a result of Bombieri, Masser and Zannier on tori, the second author proved that the intersection of a transversal curve C in a power A of a C. M. elliptic curve with the union of all algebraic subgroups of Eg of codimension 2 is finite. Here transversal means that C is not contained in any translate of an algebraic subgroup of codimension 1. We merge this result with Faltings’ theorem that C ∩ Γ is finite when Γ is a finite rank subgroup of A. We obtain the finiteness of the intersection of C with the union of all Γ + B for B an abelian subvariety of codimension 2. As a corollary, we generalize the previous result to a curve C not contained in any proper algebraic subgroup, but possibly contained in a translate. We also have weaker analog results in the non C. M. case.
Faculties and Departments:05 Faculty of Science
UniBasel Contributors:Viada, Evelina
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Oxford University Press
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:15 Nov 2017 09:10
Deposited On:22 Mar 2012 13:42

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