Elliptic Curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2004
|
| Ausgabe: | Second Edition |
| Schriftenreihe: | Graduate Texts in Mathematics
111 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject." -G. Faltings, Zentralblatt |
| Beschreibung: | 1 Online-Ressource (XXII, 490 p) |
| ISBN: | 9780387215778 9780387954905 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/b97292 |
Internformat
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| 500 | |a This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject." -G. Faltings, Zentralblatt | ||
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Datensatz im Suchindex
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| author | Husemöller, Dale |
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| building | Verbundindex |
| bvnumber | BV042418921 |
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| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/b97292 |
| edition | Second Edition |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:03Z |
| institution | BVB |
| isbn | 9780387215778 9780387954905 |
| issn | 0072-5285 |
| language | English |
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| series2 | Graduate Texts in Mathematics |
| spelling | Husemöller, Dale Verfasser aut Elliptic Curves by Dale Husemöller Second Edition New York, NY Springer New York 2004 1 Online-Ressource (XXII, 490 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 111 0072-5285 This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject." -G. Faltings, Zentralblatt Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Algebraische Geometrie (DE-588)4001161-6 s 1\p DE-604 https://doi.org/10.1007/b97292 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Husemöller, Dale Elliptic Curves Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4014487-2 |
| title | Elliptic Curves |
| title_auth | Elliptic Curves |
| title_exact_search | Elliptic Curves |
| title_full | Elliptic Curves by Dale Husemöller |
| title_fullStr | Elliptic Curves by Dale Husemöller |
| title_full_unstemmed | Elliptic Curves by Dale Husemöller |
| title_short | Elliptic Curves |
| title_sort | elliptic curves |
| topic | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie (DE-588)4001161-6 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algebraische Geometrie Elliptische Kurve |
| url | https://doi.org/10.1007/b97292 |
| work_keys_str_mv | AT husemollerdale ellipticcurves |