Number Theory III: Diophantine Geometry: Diophantine Geometry v. 3 (Encyclopaedia of Mathematical Sciences) okumak kayıt olmadan

Number Theory III: Diophantine Geometry: Diophantine Geometry v. 3 (Encyclopaedia of Mathematical Sciences)

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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.

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18,9 x 0,4 x 24,6 cm 18,9 x 0,2 x 24,6 cm WADE H MCCREE 28 Ekim 2011 18,9 x 0,5 x 24,6 cm 15 x 0,5 x 22 cm 3 Ocak 2017 30 Ekim 2011 28 Şubat 2018 18,9 x 0,6 x 24,6 cm Kolektif ERWIN N GRISWOLD ROBERT H BORK 1 Ocak 2017 Mdpi AG 29 Ekim 2011 Additional Contributors 18,9 x 0,3 x 24,6 cm

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