Berling, Heidelberg, New York: Springer Verlag, 1998. 211 pp. 23.5 x 15.5 cm. Light rubbing to covers from normal shelfwear; small bump to head of spine. Light foxing to inside of covers and edges of text block. Interior is clean and unmarked. Binding is firm. Soft Cover. Very Good.

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Detalles bibliogr�ficos

T�tulo

Model Theory and Algrbraic Geometry: An Introduction to E. Hrushovski's Proof of the Geometric Mordell-Lang Conjecture - Lecture Notes in Mathematics 1696

Editor

Springer Verlag, Berling, Heidelberg, New York

Fecha de publicaci�n

1998

Idioma

Ingl�s

ISBN 10

3540648631

ISBN 13

9783540648635

Encuadernaci�n

Paperback

Estado

Very Good

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Sinopsis

Introduction Model theorists have often joked in recent years that the part of mathemat� ical logic known as "pure model theory" (or stability theory), as opposed to the older and more traditional "model theory applied to algebra" , turns out to have more and more to do with other subjects ofmathematics and to yield gen� uine applications to combinatorial geometry, differential algebra and algebraic geometry. We illustrate this by presenting the very striking application to diophantine geometry due to Ehud Hrushovski: using model theory, he has given the first proof valid in all characteristics of the "Mordell-Lang conjecture for function fields" (The Mordell-Lang conjecture for function fields, Journal AMS 9 (1996), 667-690). More recently he has also given a new (model theoretic) proof of the Manin-Mumford conjecture for semi-abelian varieties over a number field. His proofyields the first effective bound for the cardinality ofthe finite sets involved (The Manin-Mumford conjecture, preprint). There have been previous instances of applications of model theory to alge� bra or number theory, but these appl~cations had in common the feature that their proofs used a lot of algebra (or number theory) but only very basic tools and results from the model theory side: compactness, first-order definability, elementary equivalence...

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