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Erschienen in:
2015 | OriginalPaper | Buchkapitel
A Lang Exceptional Set for Integral Points
verfasst von : Paul Vojta
Erschienen in: Geometry and Analysis on Manifolds
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In 1986 and 1991, Serge Lang defined holomorphic, diophantine, and geometric exceptional sets of a complete variety over C, over a number field, or over a field of characteristic zero, respectively, and conjectured that they should coincide when defined.
This talk examined the possibility of extending this definition to holomorphic curves or integral points in quasi-projective varieties. A central question that arises is, given an abelian (or semiabelian) variety A and a Zariskiclosed subset Z of codimension ≥ 2, can one find a nonconstant holomorphic curve in A \ Z with Zariski-dense image, or a Zariski-dense set of integral points on A \ Z? This paper proves this result for holomorphic curves (this is quite easy). For integral points, however, the question remains open. Some partial results are obtained.