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Abelian Varieties

Abelian Varieties
Catalogue Information
Field name Details
Dewey Class 512.7
Title Abelian Varieties ([EBook]) / by Serge Lang.
Author Lang, Serge. , 1927-2005
Other name(s) SpringerLink (Online service)
Publication New York, NY : Springer , 1983.
Physical Details XII, 256 pages : online resource.
ISBN 9781441985347
Contents note 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1007/978-1-4419-8534-7
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