The Arithmetic of elliptic curves
The 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 b...
Kaydedildi:
| Yazar: | |
|---|---|
| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Seri Bilgileri: | Graduate Texts in Mathematics
106 |
| Konular: | |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme de l'éditeur (Springer) Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Arithmetic of Elliptic Curves, Texte imprimé, 9780387560519 • The Arithmetic of Elliptic Curves, Texte imprimé, 9780387094939 • The arithmetic of elliptic curves, Joseph H. Silverman, 2nd edition, 2009, New York [etc.], Springer, 1 vol. (XX-513 p.), Graduate texts in mathematics, 978-0-387-09493-9 |
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| 100 | 1 | |a Silverman, Joseph H., |d 1955-...., |c mathématicien. | |
| 245 | 1 | 0 | |a The Arithmetic of elliptic curves |c by Joseph H. Silverman. |
| 260 | |a New York, NY : |b Springer New York. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Graduate Texts in Mathematics |v 106 |x 2197-5612 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 0 | |a Algebraic 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#x2013;Weil Group -- Algorithmic Aspects of Elliptic Curves. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a The 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 | |a Courbes elliptiques | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Théorie des nombres algébriques | ||
| 776 | 0 | |t The Arithmetic of Elliptic Curves |b Texte imprimé |z 9780387560519 | |
| 776 | 0 | |t The Arithmetic of Elliptic Curves |b Texte imprimé |z 9780387094939 | |
| 776 | 0 | |0 135407087 |t The arithmetic of elliptic curves |f Joseph H. Silverman |e 2nd edition |d 2009 |c New York [etc.] |n Springer |p 1 vol. (XX-513 p.) |s Graduate texts in mathematics |z 978-0-387-09493-9 | |
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