Model theory and algebraic geometry. An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture.

Bouscaren, Elisabeth:

ISBN 10: 3540648631 / ISBN 13: 9783540648635

Verlag: Berlin, Springer, 2010

Beschreibung

XV, [1], 211 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04561 9783540648635 Sprache: Englisch Gewicht in Gramm: 550. Bestandsnummer des Verkäufers 2490797

Bibliografische Details

Titel: Model theory and algebraic geometry. An ...

Verlag: Berlin, Springer

Erscheinungsdatum: 2010

Einband: Softcover

Auflage: [dodr.].

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Inhaltsangabe:

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...