Author | Lang, Serge. author |
---|---|
Title | Complex Multiplication [electronic resource] / by Serge Lang |
Imprint | New York, NY : Springer New York, 1983 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5485-0 |
Descript | VIII, 184 p. online resource |
1 Analytic Complex Multiplication -- 1. Positive Definite Involutions -- 2. CM Types and Subfields -- 3. Application to Abelian Manifolds -- 4. Construction of Abelian Manifolds with CM -- 5. Reflex of a CM Type -- 6. Application to Cyclotomic Fields -- 7. An Example: The Fermat Curve -- 2 Some Algebraic Properties of Abelian Varieties -- 1. Invariant Differential Forms -- 2. Homomorphisms and Inseparability -- 3. Reduction mod p and l-adic Representations -- 4. Reduction of Functions -- 5. Reduction of Differential Forms -- 3 Algebraic Complex Multiplication -- 1. Fields of Definition -- 2. Transformations and Multiplications -- 3. The Congruence Relation -- 4. Polarizations -- 5. Change of Riemann Forms Under Various Maps -- 6. The Main Theorem of Complex Multiplication -- 4 The CM Character -- 1. The Second Main Theorem of Complex Multiplication and the CM Character -- 2. Finite Extensions -- 3. Algebraic Properties of the Associated Characters -- 4. The CM Character over a Quadratic Subfield -- 5. Shimuraโs l-adic Representations -- 6. Application to the Zeta Function in the CM Case -- 5 Fields of Moduli, Kummer Varieties, and Descents -- 1. Fields of Moduli -- 2. General Descent -- 3. Kummer Varieties -- 4. Class Fields as Moduli Fields -- 5. Casselmanโs Theorem -- 6. Descent to a Quadratic Subfield -- 7. Further Descent Theorems -- 6 The Type Norm -- 1. The Rank of a Type -- 2. The Type Norm as Lie Homomorphism -- 3. The Image N?(Dp?) -- 4. The Type Norm as Algebraic Homomorphism -- 5. Application to Abelian Varieties -- 7 Arbitrary Conjugations of CM Types -- 1. The Reflex Norm and the Type Transfer -- 2. General Reciprocity and the Type Transfer -- 3. Application to the Conjugation of Abelian Varieties -- 4. Another Property Implying e? =1