Displaying similar documents to “Problems and results on the distribution of algebraic points on algebraic varieties”

A family of varieties with exactly one pointless rational fiber

Bianca Viray (2010)

Journal de Théorie des Nombres de Bordeaux

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We construct a concrete example of a 1 -parameter family of smooth projective geometrically integral varieties over an open subscheme of 1 such that there is exactly one rational fiber with no rational points. This makes explicit a construction of Poonen.

Quantitative versions of the Subspace Theorem and applications

Yann Bugeaud (2011)

Journal de Théorie des Nombres de Bordeaux

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During the last decade, several quite unexpected applications of the Schmidt Subspace Theorem were found. We survey some of these, with a special emphasize on the consequences of quantitative statements of this theorem, in particular regarding transcendence questions.