´úÊýȺºÍ΢»ý·Ö

Preface
Introduction

Part 1£® Algebraic Geometry
Chapter 1£®Affine and Projective Varieties
1£®1£®Affine varieties
1£®2£®Abstract affine varieties
1£®3£®Projective varieties
Exercises
Chapter 2£®Algebraic Varieties
2£®1£®Prevarieties
2£®2£®Varieties
Exercises

Part 2£® Algebraic Groups
Chapter 3£®Basic Notions
3£®1£®The notion of Mgebraic group
3£®2£®Connected algebraic groups
3£®3£®Subgroups and morphisms
3£®4£®Linearization of affine algebraic groups
3£®5£®Homogeneous spaces
3£®6£®Characters and semi-invariants
3£®7£®Quotients
Exercises
Chapter 4£®Lie Algebras and Algebraic Groups
4£®1£®Lie algebras
4£®2£®The Lie algebra of a linear algebraic group
4£®3£®Decomposition of algebraic groups
4£®4£®Solvable algebraic groups
4£®5£®Correspondence between algebraic groups and Lie algebras
4£®6£®Subgroups of SL£¨2£¬ C£©
Exercises

Part 3£® Differential Galois Theory
Chapter 5£®Picard-Vessiot Extensions
5£®1£®Derivations
5£®2£®Differential rings
5£®3£®Differential extensions
5£®4£®The ring of differential operators
5£®5£®Homogeneous linear differential equations
5£®6£®The Picard-Vessiot extension
Exercises
Chapter 6£®The Galois Correspondence
6£®1£®Differential Galois group
6£®2£®The differential Galois group as a linear algebraic group
6£®3£®The fundamental theorem of differential Galois theory
6£®4£®Liouville extensions
6£®5£®Generalized Liouville extensions
Exercises
Chapter 7£®Differential Equations over C£¨z£©
7£®1£®Fuchsian differential equations
7£®2£®Monodromy group
7£®3£®Kovacic's algorithmExercises
Chapter 8£®Suggestions for Further Reading

Bibliography
Index