E. Zeidler

Nonlinear Functional Analysis and its Applications

II/B: Nonlinear Monotone Operators
Übersetzung:Zeidler, E.; Boron, Leo F.

• Gebundenes Buch

Produktbeschreibung

This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular group r(1), including a discussion of Hekcke operators and the L-series associated to cusp forms. This is followed by a detailed study of elliptic curves with complex multiplication, their associated Grössencharacters and L-series, and applications to the construction of abelian extensions of quadratic imaginary fields. Next comes a treatment of elliptic curves over function fields and elliptic surfaces, including specialization theorems for heights and sections. This material serves as a prelude to the theory of minimal models and Néron models of elliptic curves, with a discussion of special fibers, conductors, and Ogg's formula. Next comes a brief description of q-models for elliptic curves over C and R, followed by Tate's theory of q-models for elliptic curves with non-integral j-invariant over p-adic fields. The book concludes with the construction of canonical local height functions on elliptic curves, including explicit formulas for both archimedean and non-archimedean fields.

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Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• 1989.
• Seitenzahl: 756
• Erscheinungstermin: 11. Dezember 1989
• Englisch
• Abmessung: 241mm x 160mm x 45mm
• Gewicht: 1229g
• ISBN-13: 9780387971674
• ISBN-10: 038797167X
• Artikelnr.: 22203049

Inhaltsangabe

Preface.
Introduction.
Elliptic and Modular Functions.
Complex Multiplication.
Elliptic Surfaces.
The Néron Model.
Elliptic Curves over Complete Fields.
Local Height Functions.
Appendix A: Some Useful Tables.
Notes on Exercises.
References.
List of Notation.
Index.