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Advanced Topics in the Arithmetic of Elliptic Curves, Hardcover by Silverman,...
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Item specifics
- Condition
- Book Title
- Advanced Topics in the Arithmetic of Elliptic Curves
- ISBN
- 9780387943251
- Subject Area
- Mathematics
- Publication Name
- Arithmetic of Elliptic Curves II
- Item Length
- 9.3 in
- Publisher
- Springer New York
- Subject
- Number Theory, Geometry / Algebraic, Arithmetic
- Series
- Graduate Texts in Mathematics Ser.
- Publication Year
- 1994
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Width
- 6.1 in
- Item Weight
- 34.6 Oz
- Number of Pages
- Xiii, 528 Pages
About this product
Product Information
This book is meant to be an introductory text, albeit at an upper graduate level. The main prerequisite for reading this book is some familiarity with the basic theory of elliptic curves as described, for example, in the first volume. Numerous exercises have been included at the end of each chapter. A list of comments and citations for the exercises will be found at the end of the book.
Product Identifiers
Publisher
Springer New York
ISBN-10
0387943250
ISBN-13
9780387943251
eBay Product ID (ePID)
792286
Product Key Features
Publication Name
Arithmetic of Elliptic Curves II
Format
Hardcover
Language
English
Subject
Number Theory, Geometry / Algebraic, Arithmetic
Series
Graduate Texts in Mathematics Ser.
Publication Year
1994
Type
Textbook
Subject Area
Mathematics
Number of Pages
Xiii, 528 Pages
Dimensions
Item Length
9.3 in
Item Width
6.1 in
Item Weight
34.6 Oz
Additional Product Features
LCCN
94-021787
Intended Audience
College Audience
Series Volume Number
151
Number of Volumes
1 Vol.
Lc Classification Number
Qa564-609
Table of Content
1.- I Elliptic and Modular Functions.- §1. The Modular Group.- §2. The Modular Curve X(1).- §3. Modular Functions.- §4. Uniformization and Fields of Moduli.- §5. Elliptic Functions Revisited.- §6. q-Expansions of Elliptic Functions.- §7. q-Expansions of Modular Functions.- §8. Jacobi's Product Formula for ?(?).- §9. Hecke Operators.- §10. Hecke Operators Acting on Modular Forms.- §11. L-Series Attached to Modular Forms.- Exercises.- II Complex Multiplication.- §1. Complex Multiplication over C.- §2. Rationality Questions.- §3. Class Field Theory -- A Brief Review.- §4. The Hilbert Class Field.- §5. The Maximal Abelian Extension.- §6. Integrality of j.- §7. Cyclotomic Class Field Theory.- §8. The Main Theorem of Complex Multiplication.- §9. The Associated Grössencharacter.- §10. The L-Series Attached to a CM Elliptic Curve.- Exercises.- III Elliptic Surfaces.- §1. Elliptic Curves over Function Fields.- §2. The Weak Mordell-Weil Theorem.- §3. Elliptic Surfaces.- §4. Heights on Elliptic Curves over Function Fields.- §5. Split Elliptic Surfaces and Sets of Bounded Height.- §6. The Mordell-Weil Theorem for Function Fields.- §7. The Geometry of Algebraic Surfaces.- §8. The Geometry of Fibered Surfaces.- §9. The Geometry of Elliptic Surfaces.- §10. Heights and Divisors on Varieties.- §11. Specialization Theorems for Elliptic Surfaces.- §12. Integral Points on Elliptic Curves over Function Fields.- Exercises.- IV The Néron Model.- §1. Group Varieties.- §2. Schemes and S-Schemes.- §3. Group Schemes.- §4. Arithmetic Surfaces.- §5. Néron Models.- §6. Existence of Néron Models.- §7. Intersection Theory, Minimal Models, and Blowing-Up.- §8. The Special Fiber of a Néron Model.- §9. Tate's Algorithm to Compute the Special Fiber.-§10. The Conductor of an Elliptic Curve.- §11. Ogg's Formula.- Exercises.- V Elliptic Curves over Complete Fields.- §1. Elliptic Curves over ?.- §2. Elliptic Curves over ?.- §3. The Tate Curve.- §4. The Tate Map Is Surjective.- §5. Elliptic Curves over p-adic Fields.- §6. Some Applications of p-adic Uniformization.- Exercises.- VI Local Height Functions.- §1. Existence of Local Height Functions.- §2. Local Decomposition of the Canonical Height.- §3. Archimedean Absolute Values -- Explicit Formulas.- §4. Non-Archimedean Absolute Values -- Explicit Formulas.- Exercises.- Appendix A Some Useful Tables.- §3. Elliptic Curves over ? with Complex Multiplication.- Notes on Exercises.- References.- List of Notation.
Copyright Date
1994
Dewey Decimal
516.3/52
Dewey Edition
20
Illustrated
Yes
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eBay item number:354954781264
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