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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

Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's
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Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture Paperback / softback - 1998

by E. Bouscaren

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Description

Paperback / softback. New. Illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang conjecture, this book updates developments in the applications of model theory to algebraic geometry. The detailed text includes comments and examples for the specialist and uninitiated.
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Details

  • Title Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture
  • Author E. Bouscaren
  • Binding Paperback
  • Edition Corrected
  • Condition New
  • Pages 216
  • Volumes 1
  • Language ENG
  • Publisher Springer, Berlin
  • Publication date 1998-09-17
  • Bookseller's Inventory # B9783540648635
  • ISBN 9783540648635 / 3540648631
  • Weight 0.72 lbs (0.33 kg)
  • Dimensions 9.21 x 6.14 x 0.48 in (23.39 x 15.60 x 1.22 cm)
  • Category Medical / Nursing
  • Library of Congress Catalogue Number 98038720
  • Dewey Decimal Code 511.8
  • Quantity available 10

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From the publisher

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...

First line

In this informal presentation we introduce some of the main definitions and results which form the basis of model theory.

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