Viada, Evelina. (2009) Nondense subsets of varieties in a power of an elliptic curve. International Mathematics Research Notices, 2009 (7). pp. 12131246.

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Abstract
Let E be an elliptic curve without complex multiplication (CM) deﬁned over Q. We show that on a transverse d dimensional variety V in a gpower of E, the set of algebraic points of bounded height, which are close to the union of all algebraic subgroups of E g of codimension d + 1 translated by points in a subgroup of ﬁnite rank, is Zariski nondense in V. The notion of close is deﬁned using a height function. If the subgroup of finite rank is trivial, it is sufﬁcient to assume that V is weaktransverse. This result is optimal with respect to the codimension of the algebraic subgroups. The method is based on an essentially optimal effective version of the Bogomolov Conjecture. Such an effective result is proven for subvarieties of a product of ellipitc curves. If we assume that the sets have bounded height, then we can prove that they are not Zariski dense. A conjecture, known in some special cases, claims that the sets in question have bounded height. We prove here a new case. In conclusion, our results prove a generalized case of a conjecture by Zilber and by Pink in a power of E.
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 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
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Last Modified:  28 Sep 2017 10:08 
Deposited On:  22 Mar 2012 13:42 
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