Abelian Varieties

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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. - 2. Divisorial correspondences. - Table of Notation.