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Diophantine geometry from model theory

Bulletin of Symbolic Logic 7 (1):37-57 (2001)

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[Omnibus Review].Ehud Hrushovski - 1993 - Journal of Symbolic Logic 58 (2):710-713.details Reviewed Works:B. I. Zil'ber, L. Pacholski, J. Wierzejewski, A. J. Wilkie, Totally Categorical Theories: Structural Properties and the Non-Finite Axiomatizability.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. II.B. I. Zil'ber, Strongly Minimal Countably Categorical Theories. III.B. I. Zil'ber, E. Mendelson, Totally Categorical Structures and Combinatorial Geometries.B. I. Zil'ber, The Structure of Models of Uncountably Categorical Theories. Download Export citation Bookmark 17 citations
[Omnibus Review].Anand Pillay - 1984 - Journal of Symbolic Logic 49 (1):317-321.details Download Export citation Bookmark 28 citations
A new strongly minimal set.Ehud Hrushovski - 1993 - Annals of Pure and Applied Logic 62 (2):147-166.details We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties. Download Export citation Bookmark 89 citations
The Manin–Mumford conjecture and the model theory of difference fields.Ehud Hrushovski - 2001 - Annals of Pure and Applied Logic 112 (1):43-115.details Using methods of geometric stability , we determine the structure of Abelian groups definable in ACFA, the model companion of fields with an automorphism. We also give general bounds on sets definable in ACFA. We show that these tools can be used to study torsion points on Abelian varieties; among other results, we deduce a fairly general case of a conjecture of Tate and Voloch on p-adic distances of torsion points from subvarieties. Download Export citation Bookmark 13 citations

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