{"product_id":"9783540612230","title":"Number Theory III: Diophantine Geometry","description":"\u003ch1\u003eNumber Theory III: Diophantine Geometry\u003c\/h1\u003e \u003ch2\u003eLang, Serge; Lang, Serge\u003c\/h2\u003e \u003cp\u003eIn 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.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1997-04-14\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540612230\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-58227-1\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 296\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44408133320844,"sku":"9783540612230","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540612230.jpg?v=1775758155","url":"https:\/\/lateknightbooks.com\/products\/9783540612230","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}