Cover Image
Read Now

Abelian Varieties

Bibliographic Details
Main Author: Lang, S.
Format: eBook
Language:English
Published: New York, NY Springer New York 1983, 1983
Edition:1st ed. 1983
Subjects:
Number Theory
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of 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

Similar Items