Number Theory III : Diophantine Geometry PDF
by Serge Lang
Edited by Serge Lang
Part of the Encyclopaedia of Mathematical Sciences series
Description
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.
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- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:01/12/2013
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- ISBN:9783642582271
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Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer Berlin Heidelberg
- Publication Date:01/12/2013
- Category:
- ISBN:9783642582271
