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Abelian Varieties

Author: Serge Lang
Publisher: New York, NY : Springer New York, 1983.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Serge Lang
ISBN: 9781441985347 1441985344
OCLC Number: 853267352
Description: 1 online resource (xii, 256 pages)
Contents: 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.
Responsibility: by Serge Lang.

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