Non-dense sets of subvarieties in a power of an elliptic curve

Details Non-dense sets of subvarieties in a power of an elliptic curve Non-dense sets of subvarieties in a power of an elliptic curve

2007-11-22

arxiv.org/abs/0711.3533v5

International Mathematics Reserch Notices, Vol 2009, n. 7, 1213-1246

Mathematics

Number Theory

34 pages

Scientific paper

10.1093/imrn/rnn157

Let V be an algebraic variety embedded in a power of an elliptic curve, both
defined over the algebraic numbers. We show that the set of algebraic points of
V which are of bounded height and which satisfy certain algebraic conditions
are a non-dense subset of V. This result has implications in the context of the
Pink-Zilber Conjecture and Mordel-Lang plus Bogomolov Theorem.

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