Contents
Introduction vii
Part I. General Theory
1. Schemes 3
2. Group Schemes and Representations 19
3. Induction and Injective Modules 37
4. Cohomology 49
5. Quotients and Associated Sheaves 65
6. Factor Groups 85
7. Algebras of Distributions 95
8. Representations of Finite Algebraic Groups 111
9. Representations of Frobenius Kernels 125
10. Reduction mod p 141
Part II. Representations of Reductive Groups
1. Reductive Groups 153
2. Simple G-Modules 175
3. Irreducible Representations of the Frobenius Kernels 189
4. Kempf's Vanishing Theorem 201
5. The Borel-Bott-Weil Theorem and Weyl's Character Formula 217
6. The Linkage Principle 231
7. The Translation Functors 251
8. Filtrations of Weyl Modules 267
9. Representations of GrT and GrB 291
10. Geometric Reductivity and Other Applications of the
Steinberg Modules 315
11. Injective Gr-Modules 325
12. Cohomology of the Frobenius Kernels 343
13. Schubert Schemes 353
14. Line Bundles on Schubert Schemes 365
A. Truncated Categories and Schur Algebras 385
B. Results over the Integers 411
C. Lusztig's Conjecture and Some Consequences 419
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