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Lectures on elliptic curves...
The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text
Monografía
monografia Rebiun24991684 https://catalogo.rebiun.org/rebiun/record/Rebiun24991684 m|||||o||d|||||||| cr|||||||||||| 111013s1991||||enk o ||1 0|eng|d 9781139172530 ebook) 9780521415170 hardback) 9780521425308 paperback) UPVA 998450372403706 CBUC 991010751829506709 UkCbUP eng rda UkCbUP 516.3/52 20 Cassels, J. W. S. John William Scott) author Lectures on elliptic curves J.W.S. Cassels Cambridge Cambridge University Press 1991 Cambridge Cambridge Cambridge University Press 1 online resource (vi, 137 pages) digital, PDF file(s) 1 online resource (vi, 137 pages) Text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society student texts 24 EBA Cambridge University Press Title from publisher's bibliographic system (viewed on 05 Oct 2015) The study of (special cases of) elliptic curves goes back to Diophantos and Fermat, and today it is still one of the liveliest centres of research in number theory. This book, which is addressed to beginning graduate students, introduces basic theory from a contemporary viewpoint but with an eye to the historical background. The central portion deals with curves over the rationals: the Mordell-Weil finite basis theorem, points of finite order (Nagell-Lutz) etc. The treatment is structured by the local-global standpoint and culminates in the description of the Tate-Shafarevich group as the obstruction to a Hasse principle. In an introductory section the Hasse principle for conics is discussed. The book closes with sections on the theory over finite fields (the 'Riemann hypothesis for function fields') and recently developed uses of elliptic curves for factoring large integers. Prerequisites are kept to a minimum; an acquaintance with the fundamentals of Galois theory is assumed, but no knowledge either of algebraic number theory or algebraic geometry is needed. The p-adic numbers are introduced from scratch, as is the little that is needed on Galois cohomology. Many examples and exercises are included for the reader. For those new to elliptic curves, whether they are graduate students or specialists from other fields, this will be a fine introductory text Curves, Elliptic Print version 9780521415170 London Mathematical Society student texts 24