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Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture

Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture (Paperback)

£40.99
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Synopsis

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...

Science & MathematicsMathematicsGeometryAlgebraic geometryScience & MathematicsMathematicsMathematical foundationsMathematical logicScience & MathematicsMathematicsMathematical foundationsSet theoryScience & MathematicsMathematicsNumber theory Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Publication Date: 17/09/1998 ISBN-13: 9783540648635  Details: Type: Paperback Format: Books
Availability: Printed to order. Despatched in 2-3 weeks.  

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