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Arithmetic Theory of Elliptic Curves : Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)Held in Cetaro, Italy :  Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)Held in Cetaro, Italy - J. Coates

Arithmetic Theory of Elliptic Curves : Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)Held in Cetaro, Italy

Lectures Given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.)Held in Cetaro, Italy

Paperback Published: November 1999
ISBN: 9783540665465
Number Of Pages: 264

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This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves & also contain several new results which cannot be found elsewhere in the literature. Owing to clarity & elegance of exposition & to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Fragments of the GL2 Iwasawa Theory of Elliptic Curves without Complex Multiplicationp. 1
Statement of resultsp. 2
Basic properties of the Selmer groupp. 14
Local cohomology calculationsp. 23
Global calculationsp. 39
Iwasawa Theory for Elliptic Curvesp. 51
Introductionp. 51
Kummer theory for Ep. 62
Control theoremsp. 72
Calculation of an Euler characteristicp. 85
Conclusionp. 105
Torsion Points on J0(N)and Galois Representationsp. 145
Introductionp. 145
A local study at Np. 148
The kernel of the Eisenstein idealp. 151
Lenstra's inputp. 154
Proof of Theorem 1.7p. 156
Adelic representationsp. 157
Proof of Theorem 1.6p. 163
Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyerp. 167
Quick review of elliptic curvesp. 168
Elliptic curves over Cp. 170
Elliptic curves over local fieldsp. 172
Elliptic curves over number fieldsp. 178
Elliptic curves with complex multiplicationp. 181
Descentp. 188
Elliptic unitsp. 193
Euler systemsp. 203
Bounding ideal class groupsp. 209
The theorem of Coates and Wilesp. 213
Iwasawa theory and the "main conjecture"p. 216
Computing the Selmer groupp. 227
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540665465
ISBN-10: 3540665463
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 264
Published: November 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.47
Weight (kg): 0.39

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