Rémond, Gaël and Viada, Evelina. (2003) Problème de MordellLang modulo certaines sousvariétés abéliennes. International Mathematics Research Notices, 2003 (35). pp. 19151931.

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Abstract
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 
ISSN:  10737928 
eISSN:  16870247 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  French 
Identification Number:  
edoc DOI:  
Last Modified:  15 Nov 2017 09:10 
Deposited On:  22 Mar 2012 13:42 
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