| 書(shū)目名稱 | Number Theory III | | 副標(biāo)題 | Diophantine Geometry | | 編輯 | Serge Lang | | 視頻video | http://file.papertrans.cn/669/668865/668865.mp4 | | 叢書(shū)名稱 | Encyclopaedia of Mathematical Sciences | | 圖書(shū)封面 |  | | 描述 | 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 exam | | 出版日期 | Book 1991 | | 關(guān)鍵詞 | Abelian varieties; Abelian variety; Dimension; Diophantine approximation; Divisor; elliptic curve; Isogeni | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-58227-1 | | isbn_softcover | 978-3-540-61223-0 | | isbn_ebook | 978-3-642-58227-1Series ISSN 0938-0396 | | issn_series | 0938-0396 | | copyright | Springer-Verlag Berlin Heidelberg 1991 |
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