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Omschrijving
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 ideas for 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.
Specificaties
Betrokkenen
- Auteur(s):
- Uitgeverij:
Inhoud
- Aantal bladzijden:
- 296
- Taal:
- Engels
- Reeks:
- Reeksnummer:
- nr. 60
Eigenschappen
- Productcode (EAN):
- 9783540612230
- Verschijningsdatum:
- 14/04/1997
- Uitvoering:
- Paperback
- Formaat:
- Trade paperback (VS)
- Afmetingen:
- 156 mm x 236 mm
- Gewicht:
- 453 g
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