Lehmer problem and applications
Connections for Women: Model Theory and Its Interactions with Number Theory and Arithmetic Geometry February 10, 2014 - February 11, 2014
Location: MSRI: Simons Auditorium
Lehmer conjecture predicts a lower bound for the height of a non zero algebraic integer wich is not a root of unity in terms of its degree. In this talk, we explain how the relative Lehmer problem is related to the Zilber-Pink conjecture. The idea comes from the rst article of Bombieri, Masser and Zannier on the subject : they used the lower bounds for the height given by the Lehmer problem to proove that the bounded height subset of Gn m that they were interested in, was nite. Indeed, Lehmer type bounds are used to proove that such a subset has bounded degree and by Northcott property they conlcuded niteness. We'll explain how this argument works in the context of abelian varieties.
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