000			02611nam a22003498i 4500
001			CR9781139172530
003			UkCbUP
005			20200124160221.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			111013s1991||||enk o ||1 0|eng|d
020			_a9781139172530 (ebook)
020			_z9780521415170 (hardback)
020			_z9780521425308 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA567.2.E44 _bC38 1991
082	0	0	_a516.3/52 _220
100	1		_aCassels, J. W. S. _q(John William Scott), _eauthor.
245	1	0	_aLectures on elliptic curves / _cJ.W.S. Cassels.
264		1	_aCambridge : _bCambridge University Press, _c1991.
300			_a1 online resource (vi, 137 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society student texts ; _v24
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
520			_aThe 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.
650		0	_aCurves, Elliptic.
776	0	8	_iPrint version: _z9780521415170
830		0	_aLondon Mathematical Society student texts ; _v24.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139172530
999			_c516726 _d516724