Algebraic Groups The Theory of Group Schemes of Finite Type over a Field 1st Edition J. S. Milne

1 Definitions and Basic Properties

2 Examples and Basic Constructions

3 Affine Algebraic Groups and Hopf Algebras

4 Linear Representations of Algebraic Groups

5 Group Theory; the Isomorphism Theorems

6 Subnormal Series; Solvable and Nilpotent Algebraic Groups

7 Algebraic Groups Acting on Schemes

8 The Structure of General Algebraic Groups

9 Tannaka Duality; Jordan Decompositions

10 The Lie Algebra of an Algebraic Group

11 Finite Group Schemes

12 Groups of Multiplicative Type; Linearly Reductive Groups

13 Tori Acting on Schemes

14 Unipotent Algebraic Groups

15 Cohomology and Extensions

16 The Structure of Solvable Algebraic Groups

17 Borel Subgroups and Applications

18 The Geometry of Algebraic Groups

19 Semisimple and Reductive Groups

20 Algebraic Groups of Semisimple Rank One

21 Split Reductive Groups

22 Representations of Reductive Groups

23 The Isogeny and Existence Theorems

24 Construction of the Semisimple Groups