Displaying similar documents to “Diophantine approximation and deformation”

Division-ample sets and the Diophantine problem for rings of integers

Gunther Cornelissen, Thanases Pheidas, Karim Zahidi (2005)

Journal de Théorie des Nombres de Bordeaux

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We prove that Hilbert’s Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called set of integers and of an elliptic curve of rank one over K ). We relate division-ample sets to arithmetic of abelian varieties.

Diophantine approximation on algebraic varieties

Michael Nakamaye (1999)

Journal de théorie des nombres de Bordeaux

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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.