Lectures on elliptic curves /
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| Author / Creator: | Cassels, J. W. S. (John William Scott) |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, 1991. |
| Description: | 1 online resource (vi, 137 pages) |
| Language: | English |
| Series: | London Mathematical Society student texts ; 24 London Mathematical Society student texts ; 24. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11200377 |
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| 100 | 1 | |a Cassels, J. W. S. |q (John William Scott) |0 http://id.loc.gov/authorities/names/n50035233 | |
| 245 | 1 | 0 | |a Lectures on elliptic curves / |c J.W.S. Cassels. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1991. | ||
| 300 | |a 1 online resource (vi, 137 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society student texts ; |v 24 | |
| 504 | |a Includes bibliographical references (page 135) and index. | ||
| 505 | 0 | 0 | |g 1 |t Curves of genus 0. Introduction |g 3 -- |g 2 |t p-adic numbers |g 6 -- |g 3 |t Local-global principle for conics |g 13 -- |g 4 |t Geometry of numbers |g 17 -- |g 5 |t Local-global principle. Conclusion of proof |g 20 -- |g 6 |t Cubic curves |g 23 -- |g 7 |t Non-singular cubics. The group law |g 27 -- |g 8 |t Elliptic curves. Canonical form |g 32 -- |g 9 |t Degenerate laws |g 39 -- |g 10 |t Reduction |g 42 -- |g 11 |t P-adic case |g 46 -- |g 12 |t Global torsion |g 50 -- |g 13 |t Finite basis theorem. Strategy and comments |g 54 -- |g 14 |t A 2-isogeny |g 58 -- |g 15 |t Weak finite basis theory |g 66 -- |g 16 |t Remedial mathematics. Resultants |g 75 -- |g 17 |t Heights. Finite basis Theorem |g 78 -- |g 18 |t Local-global for genus 1 |g 85 -- |g 19 |t Elements of Galois cohomology |g 89 -- |g 20 |t Construction of the jacobian |g 92 -- |g 21 |t Some abstract nonsense |g 98 -- |g 22 |t Principal homogeneous spaces and Galois cohomology |g 104 -- |g 23 |t Tate-Shafarevich group |g 108 -- |g 24 |t Endomorphism group |g 114 -- |g 25 |t Points over finite fields |g 118 -- |g 26 |t Factorizing using elliptic curves |g 124. |
| 588 | 0 | |a Print version record. | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Curves, Elliptic. |0 http://id.loc.gov/authorities/subjects/sh85034918 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Algebraic. |2 bisacsh | |
| 650 | 7 | |a Curves, Elliptic. |2 fast |0 (OCoLC)fst00885455 | |
| 650 | 7 | |a Diophantische Gleichung |2 gnd |0 http://d-nb.info/gnd/4012386-8 | |
| 650 | 7 | |a Elliptische Kurve |2 gnd |0 http://d-nb.info/gnd/4014487-2 | |
| 650 | 1 | 7 | |a Elliptische functies. |2 gtt |
| 650 | 7 | |a Courbes elliptiques. |2 ram | |
| 650 | 7 | |a Elliptiske kurver. |2 tekord | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Cassels, J.W.S. (John William Scott). |t Lectures on elliptic curves. |d Cambridge ; New York : Cambridge University Press, 1991 |z 0521415179 |w (DLC) 92160903 |w (OCoLC)25160885 |
| 830 | 0 | |a London Mathematical Society student texts ; |v 24. |0 http://id.loc.gov/authorities/names/n84727069 | |
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| 928 | |t Library of Congress classification |a QA567.2.E44 C38 1991eb |l Online |c UC-FullText |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=e000xna&AN=570389 |z eBooks on EBSCOhost |g ebooks |i 12392778 | ||