Model Theory and Algebraic Geometry

€ 47,99
Lieferbar innerhalb von 2-3 Tagen
Oktober 1999



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...


to model theory.
to stability theory and Morley rank.
Omega-stable groups.
Model theory of algebraically closed fields.
to abelian varieties and the Mordell-Lang conjecture.
The model-theoretic content of Lang's conjecture.
Zariski geometries.
Differentially closed fields.
Separably closed fields.
Proof of the Mordell-Lang conjecture for function fields.
Proof of Manin's theorem by reduction to positive characteristic.
EAN: 9783540648635
ISBN: 3540648631
Untertitel: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture. 1st ed. 1998. Corr. 2nd printing 1999. Book. Sprache: Englisch.
Verlag: Springer
Erscheinungsdatum: Oktober 1999
Seitenanzahl: 228 Seiten
Format: kartoniert
Es gibt zu diesem Artikel noch keine Bewertungen.Kundenbewertung schreiben