Modular Forms and Fermat’s Last Theorem:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1997
|
| Schlagworte: | |
| Online-Zugang: | Volltext Buchcover |
| Beschreibung: | This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem |
| Beschreibung: | 1 Online-Ressource (XIX, 582 p) |
| ISBN: | 9781461219743 9780387989983 |
| DOI: | 10.1007/978-1-4612-1974-3 |
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Datensatz im Suchindex
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| author | Cornell, Gary |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1974-3 |
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| spelling | Cornell, Gary Verfasser aut Modular Forms and Fermat’s Last Theorem edited by Gary Cornell, Joseph H. Silverman, Glenn Stevens New York, NY Springer New York 1997 1 Online-Ressource (XIX, 582 p) txt rdacontent c rdamedia cr rdacarrier This volume contains expanded versions of lectures given at an instructional conference on number theory and arithmetic geometry held August 9 through 18, 1995 at Boston University. Contributor's includeThe purpose of the conference, and of this book, is to introduce and explain the many ideas and techniques used by Wiles in his proof that every (semi-stable) elliptic curve over Q is modular, and to explain how Wiles' result can be combined with Ribet's theorem and ideas of Frey and Serre to show, at long last, that Fermat's Last Theorem is true. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions, modular curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of Wiles' proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serre's conjectures, Galois deformations, universal deformation rings, Hecke algebras, complete intersections and more, as the reader is led step-by-step through Wiles' proof. In recognition of the historical significance of Fermat's Last Theorem, the volume concludes by looking both forward and backward in time, reflecting on the history of the problem, while placing Wiles' theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this volume to be an indispensable resource for mastering the epoch-making proof of Fermat's Last Theorem Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Modulform (DE-588)4128299-1 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Fermatsche Vermutung (DE-588)4154012-8 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1995 Boston Mass. gnd-content Elliptische Kurve (DE-588)4014487-2 s Modulform (DE-588)4128299-1 s Arithmetische Geometrie (DE-588)4131383-5 s Fermatsche Vermutung (DE-588)4154012-8 s 2\p DE-604 Zahlentheorie (DE-588)4067277-3 s Algebraische Geometrie (DE-588)4001161-6 s 3\p DE-604 Silverman, Joseph H. Sonstige oth Stevens, Glenn Sonstige oth https://doi.org/10.1007/978-1-4612-1974-3 Verlag Volltext SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027855363&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Buchcover 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cornell, Gary Modular Forms and Fermat’s Last Theorem Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Modulform (DE-588)4128299-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Elliptische Kurve (DE-588)4014487-2 gnd Fermatsche Vermutung (DE-588)4154012-8 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4128299-1 (DE-588)4001161-6 (DE-588)4067277-3 (DE-588)4014487-2 (DE-588)4154012-8 (DE-588)4131383-5 (DE-588)1071861417 |
| title | Modular Forms and Fermat’s Last Theorem |
| title_auth | Modular Forms and Fermat’s Last Theorem |
| title_exact_search | Modular Forms and Fermat’s Last Theorem |
| title_full | Modular Forms and Fermat’s Last Theorem edited by Gary Cornell, Joseph H. Silverman, Glenn Stevens |
| title_fullStr | Modular Forms and Fermat’s Last Theorem edited by Gary Cornell, Joseph H. Silverman, Glenn Stevens |
| title_full_unstemmed | Modular Forms and Fermat’s Last Theorem edited by Gary Cornell, Joseph H. Silverman, Glenn Stevens |
| title_short | Modular Forms and Fermat’s Last Theorem |
| title_sort | modular forms and fermat s last theorem |
| topic | Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Modulform (DE-588)4128299-1 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Zahlentheorie (DE-588)4067277-3 gnd Elliptische Kurve (DE-588)4014487-2 gnd Fermatsche Vermutung (DE-588)4154012-8 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Mathematics Geometry, algebraic Number theory Number Theory Algebraic Geometry Mathematik Modulform Algebraische Geometrie Zahlentheorie Elliptische Kurve Fermatsche Vermutung Arithmetische Geometrie Konferenzschrift 1995 Boston Mass. |
| url | https://doi.org/10.1007/978-1-4612-1974-3 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027855363&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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