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Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture - Couverture souple
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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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Model theory and algebraic geometry. An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture.
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Model Theory and Algebraic Geometry : An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture
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Springer Berlin Heidelberg, 1999
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ISBN 13 : 9783540648635
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Model Theory and Algrbraic Geometry: An Introduction to E. Hrushovski's Proof of the Geometric Mordell-Lang Conjecture - Lecture Notes in Mathematics 1696
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Paperback. Etat : Very Good. 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. N° de réf. du vendeur 625221
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Model Theory and Algebraic Geometry
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Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture (Lecture Notes in Mathematics, 1696)
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Model Theory and Algebraic Geometry : An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture
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Model Theory and Algebraic Geometry : An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture
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Springer Berlin Heidelberg, 1998
ISBN 10 : 3540648631
ISBN 13 : 9783540648635
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783540648635
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Model Theory and Algebraic Geometry
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Springer Berlin Heidelberg Sep 1998, 1998
ISBN 10 : 3540648631
ISBN 13 : 9783540648635
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 228 pp. Englisch. N° de réf. du vendeur 9783540648635
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Model Theory and Algebraic Geometry: An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture (Lecture Notes in Mathematics, 1696)
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Model Theory and Algebraic Geometry
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Springer Berlin Heidelberg, Springer Berlin Heidelberg Sep 1998, 1998
ISBN 10 : 3540648631
ISBN 13 : 9783540648635
Neuf
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Taschenbuch. Etat : Neu. Neuware -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. 228 pp. Englisch. N° de réf. du vendeur 9783540648635
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