Hilbert's Tenth Problem: Relations With Arithmetic and Algebraic Geometry : Workshop on Hilbert's Tenth Problem : Relations With Arithemtic and Algebraic Geometry November 2-5 [Paperback]

Jan Denef (Editor), Leonard Lipshitz (Editor), Thanases Pheidas (Editor), Jan Van Geel (Editor)

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Product Details

Paperback: 367 pages
Publisher: American Mathematical Society; 1 edition (2000)
Language: English
ISBN-10: 0821826220
ISBN-13: 978-0821826225
Product Dimensions: 25.2 x 17.8 x 2 cm
Shipping Weight: 440 g

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Product Description

Book Description

This book is the result of a meeting that took place at the University of Ghent (Belgium) on the relations between Hilbert's tenth problem, arithmetic, and algebraic geometry. Included are written articles detailing the lectures that were given as well as contributed papers on current topics of interest.

The following areas are addressed: an historical overview of Hilbert's tenth problem, Hilbert's tenth problem for various rings and fields, model theory and local-global principles, including relations between model theory and algebraic groups and analytic geometry, conjectures in arithmetic geometry and the structure of diophantine sets, for example with Mazur's conjecture, Lang's conjecture, and Bücchi's problem, and results on the complexity of diophantine geometry, highlighting the
relation to the theory of computation.

The volume allows the reader to learn and compare different approaches (arithmetical, geometrical, topological, model-theoretical, and computational) to the general structural analysis of the set of solutions of polynomial equations. It would make a nice contribution to graduate and advanced graduate courses on logic, algebraic geometry, and number theory.