Viada, Evelina. (2010) Lower bounds for the normalized height and nondense subsets of varieties in an abelian variety. International journal of number theory, Vol. 6, H. 3. pp. 471499.

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Abstract
This work is the third part of a series of papers. In the ﬁrst two we considered curves and varieties in a power of an elliptic curve. Here we deal with subvarieties of an abelian variety in general. Let V be an irreducible variety of dimension d embedded in an abelian variety A, both deﬁned over the algebraic numbers. We say that V is weaktransverse if V is not contained in any proper algebraic subgroup of A, and transverse if it is not contained in any translate of such a subgroup. Assume a conjectural lower bound for the normalized height of V . Then, for V transverse, we prove that the algebraic points of bounded height of V which lie in the union of all algebraic subgroups of A of codimension at least d + 1 translated by the points close to a subgroup Γ of ﬁnite rank, are non Zariskidense in V . If Γ has rank zero, it is sufficient to assume that V is weaktransverse. The notion of closeness is deﬁned using a height function.
Faculties and Departments:  05 Faculty of Science 

UniBasel Contributors:  Viada, Evelina 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  World Scientific 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
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Last Modified:  31 Dec 2015 10:45 
Deposited On:  22 Mar 2012 13:51 
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