Cyclotomic Fields II

Inhaltsverzeichnis

• Volume II.
• 10 Measures and Iwasawa Power Series.
• 1. Iwasawa Invariants for Measures.
• 2. Application to the Bernoulli Distributions.
• 3. Class Numbers as Products of Bernoulli Numbers.
• 4. Divisibility by l Prime to p: Washington’s Theorem.
• 11 The Ferrero-Washington Theorems.
• 1. Basic Lemma and Applications.
• 2. Equidistribution and Normal Families.
• 3. An Approximation Lemma.
• 4. Proof of the Basic Lemma.
• 12 Measures in the Composite Case.
• 1. Measures and Power Series in the Composite Case.
• 2. The Associated Analytic Function on the Formal Multiplicative Group.
• 3. Computation of Lp(l, x) in the Composite Case.
• 13 Divisibility of Ideal Class Numbers.
• 1. Iwasawa Invariants in Zp-extensions.
• 2. CM Fields, Real Subfields, and Rank Inequalities.
• 3. The l-primary Part in an Extension of Degree Prime to l.
• 4. A Relation between Certain Invariants in a Cyclic Extension.
• 5. Examples of Iwasawa.
• 6. A Lemma of Kummer.
• 14 p-adic Preliminaries.
• 1. The p-adic Gamma Function.
• 2. The Artin-Hasse Power Series.
• 3. Analytic Representation of Roots of Unity.
• 15 The Gamma Function and Gauss Sums.
• 1. The Basic Spaces.
• 2. The Frobenius Endomorphism.
• 3. The Dwork Trace Formula and Gauss Sums.
• 4. Eigenvalues of the Frobenius Endomorphism and the p-adic Gamma Function.
• 5. p-adic Banach Spaces.
• 16 Gauss Sums and the Artin-Schreier Curve.
• 1. Power Series with Growth Conditions.
• 2. The Artin-Schreier Equation.
• 3. Washnitzer-Monsky Cohomology.
• 4. The Frobenius Endomorphism.
• 17 Gauss Sums as Distributions.
• 1. The Universal Distribution.
• 2. The Gauss Sums as Universal Distributions.
• 3. The L-function at s = 0.
• 4. The p-adic Partial Zeta Function.