Abelian Varieties

Inhaltsverzeichnis

• I Algebraic Groups.
• 1. Groups, subgroups, and factor groups.
• 2. Intersections and Pontrjagin products.
• 3. The field of definition of a group variety.
• II General Theorems on Abelian Varieties.
• 1. Rational maps of varieties into abelian varieties.
• 2. The Jacobian variety of a curve.
• 3. The Albanese variety.
• III The Theorem of the Square.
• 1. Algebraic equivalence.
• 2. The theorem of the cube and the theorem of the square.
• 3. The theorem of the square for groups.
• 4. The kernel in the theorem of the square.
• IV Divisor Classes on an Abelian Variety.
• 1. Applications of the theorem of the square to abelian varieties.
• 2. The torsion group.
• 3. Numerical equivalence.
• 4. The Picard variety of an abelian variety.
• V Functorial Formulas.
• 1. The transpose of a homomorphism.
• 2. A list of formulas and commutative diagrams.
• 3. The involutions.
• VI The Picard Variety of an Arbitrary Variety.
• 1. Construction of the Picard variety.
• 2. Divisorial correspondences.
• 3. Application to the theory of curves.
• 4. Reciprocity and correspondences.
• VII The l-Adic Representations.
• 1. The l-adic spaces.
• 2. Dual representations.
• VIII Algebraic Systems of Abelian Varieties.
• 1. The K/k-image.
• 2. The generic hyperplane section.
• 3. The K/k-trace.
• 4. The transpose of an exact sequence.
• 5. Duality between image and trace.
• 6. Exact sequences of varieties.
• Appendix Composition of Correspondences.
• 1. Inverse images.
• Table of Notation.