04013nam 22006855 450 991014630620332120250731082137.03-540-68521-910.1007/978-3-540-68521-0(CKB)1000000000437316(SSID)ssj0000324886(PQKBManifestationID)12124433(PQKBTitleCode)TC0000324886(PQKBWorkID)10322481(PQKB)11216380(DE-He213)978-3-540-68521-0(MiAaPQ)EBC3088526(MiAaPQ)EBC6485915(PPN)155184598(BIP)47731173(EXLCZ)99100000000043731620121227d1998 u| 0engurnn#008mamaatxtccrModel Theory and Algebraic Geometry An introduction to E. Hrushovski's proof of the geometric Mordell-Lang conjecture /edited by Elisabeth Bouscaren1st ed. 1998.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1998.1 online resource (XVI, 216 p.)Lecture Notes in Mathematics,1617-9692 ;1696Bibliographic Level Mode of Issuance: Monograph3-540-64863-1 Includes bibliographical references at the end of each chapters and index.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.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...Lecture Notes in Mathematics,1617-9692 ;1696Geometry, AlgebraicLogic, Symbolic and mathematicalNumber theoryAlgebraic GeometryMathematical Logic and FoundationsNumber TheoryGeometry, Algebraic.Logic, Symbolic and mathematical.Number theory.Algebraic Geometry.Mathematical Logic and Foundations.Number Theory.516.3503C60mscBouscaren Elisabeth1956-MiAaPQMiAaPQMiAaPQBOOK9910146306203321Model theory and algebraic geometry78161UNINA02517oas 2201093 a 450 991033313310332120251202023711.01878-3570(DE-599)ZDB2102813-8(DE-599)2102813-8(OCoLC)38371891(CONSER) 2009233338(CKB)954925376872(EXLCZ)9995492537687219980209b19252011 sy aengurmnu||||||||txtrdacontentcrdamediacrrdacarrierJournal of the American Dietetic AssociationChicago American Dietetic AssociationRefereed/Peer-reviewed0002-8223 J Am Diet AssocJ. Am. Diet. Assoc.DietPeriodicalsDiet in diseasePeriodicalsDietDieteticsAlimentationPériodiquesRégimes alimentairesPériodiquesDietfast(OCoLC)fst00893284Diet in diseasefast(OCoLC)fst00893314Periodical.Periodicals.fastDietDiet in diseaseDiet.Dietetics.AlimentationRégimes alimentairesDiet.Diet in disease.613.205American Dietetic AssociationFGAFGAOCLOCLCQCOUCUSOCLCQDLCOCLCQEBVOCLCQUV0AUDQE2GUATEFOCLCQWAUUKMGBAGLOCLCQOPELSOCLCFCOOOCLCOOCLCQOCLCOOCLCQTSCOCLCABUFAU@OCLCOWYUU3WVT2OCLCOOCLCQUEJOCLCQIOYOCLCLEZAOCLCQJOURNAL9910333133103321Journal of the American Dietetic Association794252UNINA