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Beschreibung
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to… suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideasfor the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more. 106,99 €
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Technische Daten
Erscheinungsdatum
14.04.1997
Sprache
Englisch
EAN
9783540612230
Herausgeber
Springer Berlin
Sonderedition
Nein
Autor
Serge Lang
Seitenanzahl
296
Einbandart
Broschiert
Buch Untertitel
Diophantine Geometry
Schlagwörter
Abelian varieties, Abelian variety, Dimension, Diophantine approximation, Divisor, elliptic curve, Isogenie, number theory, sheaves
Thema-Inhalt
PBH - Zahlentheorie
PBMW - Algebraische Geometrie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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