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Preface 6 Contents 14 1 Nontriviality of Arithmetic Invariants 20 1.1 Arithmetic Invariants in Iwasawa Theory 22 1.1.1 Iwasawa Invariant 23 1.1.2 L-Invariant 24 1.2 Dirichlet L-Values 29 1.2.1 A Nonvanishing Result for Dirichlet L-Values 30 1.2.2 Hecke Operators for Gm 32 1.2.3 Measure Associated with a U(l)-Eigenfunction 34 1.2.4 Evaluation Formula 36 1.2.5 Zariski Density 37 1.2.6 Proof of Theorem 1.8 39 1.3 CM Periods and L-Values 40 1.3.1 Elliptic Modular Forms 42 1.3.2 A Rationality Theorem, an Application 46 1.3.3 p-Adic Elliptic Modular Form 48 1.3.4 CM Elliptic Curve 50 1.3.5 Invariant Differential Operators 52 1.3.6 p-Adic Differential Operators 54 1.3.7 Katz Measure at a Glance 58 2 Elliptic Curves and Modular Forms 62 2.1 Curves over a Field 62 2.1.1 Plane Curves 62 2.1.2 Tangent Space and Local Rings 66 2.1.3 Projective Space 70 2.1.4 Projective Plane Curve 71 2.1.5 Divisors 73 2.1.6 Riemann–Roch Theorem 75 2.1.7 Regular Maps from a Curve into a Projective Space 77 2.2 Elliptic Curves 77 2.2.1 Abel's Theorem 77 2.2.2 Weierstrass Equations of Elliptic Curves 79 2.2.3 Moduli of Weierstrass Type 81 2.3 Modular Forms 83 2.3.1 Elliptic Curves over General Rings 84 2.3.2 Geom

Who reads Elliptic Curves and Arithmetic Invariants?

Author

Haruzo Hida (auth.)

Publisher

Springer

Published

2013

Language

EN

Category

nonfiction