000			03349nam a22004575i 4500
001			978-0-387-09494-6
003			DE-He213
005			20260129123625.0
007			cr nn 008mamaa
008			100301s2009 xxu| s |||| 0|eng d
020			_a9780387094946
020			_a99780387094946
024	7		_a10.1007/978-0-387-09494-6 _2doi
040			_cCICY
100	1		_aSilverman, Joseph H. _eauthor.
245	1	4	_aThe Arithmetic of Elliptic Curves _h[recurso electrónico] / _cby Joseph H. Silverman.
264		1	_aNew York, NY : _bSpringer New York, _c2009.
300			_aXX, 514 p. 14 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aGraduate Texts in Mathematics, _x0072-5285 ; _v106
505	0		_aAlgebraic Varieties -- Algebraic Curves -- The Geometry of Elliptic Curves -- The Formal Group of an Elliptic Curve -- Elliptic Curves over Finite Fields -- Elliptic Curves over C -- Elliptic Curves over Local Fields -- Elliptic Curves over Global Fields -- Integral Points on Elliptic Curves -- Computing the Mordell-Weil Group -- Algorithmic Aspects of Elliptic Curves.
520			_aThe theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, and elliptic curves over finite fields, the complex numbers, local fields, and global fields. Included are proofs of the Mordell-Weil theorem giving finite generation of the group of rational points and Siegel's theorem on finiteness of integral points. For this second edition of The Arithmetic of Elliptic Curves, there is a new chapter entitled Algorithmic Aspects of Elliptic Curves, with an emphasis on algorithms over finite fields which have cryptographic applications. These include Lenstra's factorization algorithm, Schoof's point counting algorithm, Miller's algorithm to compute the Tate and Weil pairings, and a description of aspects of elliptic curve cryptography. There is also a new section on Szpiro's conjecture and ABC, as well as expanded and updated accounts of recent developments and numerous new exercises. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.
650		0	_aMATHEMATICS.
650		0	_aALGEBRA.
650		0	_aGEOMETRY, ALGEBRAIC.
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aALGEBRAIC GEOMETRY.
650	2	4	_aNUMBER THEORY.
650	2	4	_aALGEBRA.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387094939
830		0	_aGraduate Texts in Mathematics, _x0072-5285 ; _v106
856	4	0	_uhttp://dx.doi.org/10.1007/978-0-387-09494-6 _zVer el texto completo en las instalaciones del CICY
942			_2ddc _cER
999			_c55941 _d55941