Algebraic geometry IV (Enc.Math.55, Springer 1994)

Contents......Page all_29622_to_00288.cpc0005.djvu
Historical Comments......Page all_29622_to_00288.cpc0008.djvu
1.2. Morphisms......Page all_29622_to_00288.cpc0011.djvu
1.6. Non-Affine Varieties......Page all_29622_to_00288.cpc0012.djvu
2.1. The Definition of a Linear Algebraic Group......Page all_29622_to_00288.cpc0013.djvu
2.2. Some Basic Facts......Page all_29622_to_00288.cpc0017.djvu
2.3. G-Spaces......Page all_29622_to_00288.cpc0018.djvu
2.4. The Lie Algebra of an Algebraic Group......Page all_29622_to_00288.cpc0020.djvu
2.5. Quotients......Page all_29622_to_00288.cpc0022.djvu
§3. Structural Properties of Linear Algebraic Groups......Page all_29622_to_00288.cpc0023.djvu
3.1. Jordan Decomposition and Related Results......Page all_29622_to_00288.cpc0024.djvu
3.2. Diagonalizable Groups and Tori......Page all_29622_to_00288.cpc0025.djvu
3.4. Connected Solvable Groups......Page all_29622_to_00288.cpc0027.djvu
3.5. Parabolic Subgroups and Borel Subgroups......Page all_29622_to_00288.cpc0029.djvu
4.1. Groups of Rank One......Page all_29622_to_00288.cpc0032.djvu
4.2. The Root Datum and the Root System......Page all_29622_to_00288.cpc0034.djvu
4.3. Basic Properties of Reductive Groups......Page all_29622_to_00288.cpc0037.djvu
4.4. Existence and Uniqueness Theorems for Reductive Groups......Page all_29622_to_00288.cpc0041.djvu
4.5. Classification of Quasi-simple Linear Algebraic Groups......Page all_29622_to_00288.cpc0043.djvu
4.6. Representation Theory......Page all_29622_to_00288.cpc0046.djvu
1.1. F-Structures on Affine Varieties......Page all_29622_to_00288.cpc0052.djvu
1.2. F-Structures on Arbitrary Varieties......Page all_29622_to_00288.cpc0053.djvu
1.3. Forms......Page all_29622_to_00288.cpc0054.djvu
1.4. Restriction of the Ground Field......Page all_29622_to_00288.cpc0055.djvu
2.1. Generalities About F-Groups......Page all_29622_to_00288.cpc0056.djvu
2.2. Quotients......Page all_29622_to_00288.cpc0058.djvu
2.3. Forms......Page all_29622_to_00288.cpc0059.djvu
2.4. Restriction of the Ground Field......Page all_29622_to_00288.cpc0060.djvu
3.1. F-Tori......Page all_29622_to_00288.cpc0061.djvu
3.2. F-Tori in F-Groups......Page all_29622_to_00288.cpc0063.djvu
3.3. Split Tori in F-Groups......Page all_29622_to_00288.cpc0064.djvu
4.1. Solvable Groups......Page all_29622_to_00288.cpc0065.djvu
4.2. Sections......Page all_29622_to_00288.cpc0066.djvu
4.3. Elementary Unipotent Groups......Page all_29622_to_00288.cpc0067.djvu
4.5. Basic Results About Solvable F-Groups......Page all_29622_to_00288.cpc0068.djvu
5.1. Split Reductive Groups......Page all_29622_to_00288.cpc0069.djvu
5.2. Parabolic Subgroups......Page all_29622_to_00288.cpc0070.djvu
5.3. The Small Root System......Page all_29622_to_00288.cpc0072.djvu
5.4. The Groups G(F)......Page all_29622_to_00288.cpc0076.djvu
5.5. The Spherical Tits Building of a Reductive F-Group......Page all_29622_to_00288.cpc0078.djvu
6.1. Isomorphism Theorem......Page all_29622_to_00288.cpc0079.djvu
6.2. Existence......Page all_29622_to_00288.cpc0081.djvu
6.3. Representation Theory of F-Groups......Page all_29622_to_00288.cpc0088.djvu
1.1. Algebraic Subalgebras......Page all_29622_to_00288.cpc0090.djvu
2.1. Locally Compact Fields......Page all_29622_to_00288.cpc0092.djvu
2.2. Real Lie Groups......Page all_29622_to_00288.cpc0095.djvu
3.1. Lang\'s Theorem and its Consequences......Page all_29622_to_00288.cpc0098.djvu
3.2. Finite Groups of Lie Type......Page all_29622_to_00288.cpc0101.djvu
3.3. Representations of Finite Groups of Lie Type......Page all_29622_to_00288.cpc0103.djvu
4.1. The Apartment and Affine Dynkin Diagram......Page all_29622_to_00288.cpc0105.djvu
4.2. The Affine Building......Page all_29622_to_00288.cpc0108.djvu
4.3. Tits System, Decompositions......Page all_29622_to_00288.cpc0111.djvu
4.4. Local Fields......Page all_29622_to_00288.cpc0112.djvu
5.1. Adele Groups......Page all_29622_to_00288.cpc0113.djvu
5.2. Reduction Theory......Page all_29622_to_00288.cpc0116.djvu
5.3. Finiteness Results......Page all_29622_to_00288.cpc0119.djvu
References......Page all_29622_to_00288.cpc0122.djvu
Contents......Page all_29622_to_00288.cpc0127.djvu
Conventions and Notation......Page all_29622_to_00288.cpc0131.djvu
0.1. The Subject of Invariant Theory......Page all_29622_to_00288.cpc0133.djvu
0.2. Sources of Invariant Theory......Page all_29622_to_00288.cpc0135.djvu
0.3. Geometric Methods......Page all_29622_to_00288.cpc0136.djvu
0.4. Invariants of the Symmetric Group......Page all_29622_to_00288.cpc0137.djvu
0.6. Invariants of a Linear Operator......Page all_29622_to_00288.cpc0138.djvu
0.7. Unimodular Invariants of a Quadratic Form......Page all_29622_to_00288.cpc0139.djvu
0.9. Invariants of a System of Vectors......Page all_29622_to_00288.cpc0140.djvu
0.10. Applications to Projective Geometry......Page all_29622_to_00288.cpc0142.djvu
0.12. Invariants of Binary Forms......Page all_29622_to_00288.cpc0144.djvu
0.13. Invariants of Binary Polyhedral Groups......Page all_29622_to_00288.cpc0146.djvu
0.14. Invariants of a Ternary Cubic Form......Page all_29622_to_00288.cpc0149.djvu
1.1. Regular and Rational Actions......Page all_29622_to_00288.cpc0150.djvu
1.2. Embedding Theorems......Page all_29622_to_00288.cpc0152.djvu
1.3. Orbits......Page all_29622_to_00288.cpc0153.djvu
1.4. Stabilizers......Page all_29622_to_00288.cpc0155.djvu
1.5. Inheritance of Orbits......Page all_29622_to_00288.cpc0156.djvu
2.1. Introduction......Page all_29622_to_00288.cpc0157.djvu
2.2. The Graph of an Action......Page all_29622_to_00288.cpc0158.djvu
2.3. Separation of Orbits in General Position......Page all_29622_to_00288.cpc0159.djvu
2.4. Rational Quotient......Page all_29622_to_00288.cpc0160.djvu
2.5. Sections......Page all_29622_to_00288.cpc0161.djvu
2.7. Birational Classification of Actions......Page all_29622_to_00288.cpc0163.djvu
2.8. Relative Sections......Page all_29622_to_00288.cpc0164.djvu
2.9. The Rationality Problem......Page all_29622_to_00288.cpc0166.djvu
3.1. Introduction......Page all_29622_to_00288.cpc0168.djvu
3.2. Connection Between Integral and Rational Invariants......Page all_29622_to_00288.cpc0169.djvu
3.3. Basic Invariants......Page all_29622_to_00288.cpc0170.djvu
3.4. Hilbert\'s Theorem on Invariants......Page all_29622_to_00288.cpc0172.djvu
3.5. Constructive Invariant Theory......Page all_29622_to_00288.cpc0173.djvu
3.6. Hilbert\'s Fourteenth Problem......Page all_29622_to_00288.cpc0174.djvu
3.7. Grosshans Subgroups......Page all_29622_to_00288.cpc0175.djvu
3.8. Chevalley Sections......Page all_29622_to_00288.cpc0177.djvu
3.9. Properties of the Algebra of Invariants......Page all_29622_to_00288.cpc0180.djvu
3.10. Facts about Poincare Series......Page all_29622_to_00288.cpc0181.djvu
3.11. The Poincare Series of the Algebra of Invariants......Page all_29622_to_00288.cpc0183.djvu
3.12. Covariants......Page all_29622_to_00288.cpc0185.djvu
3.13. The Global Module of Covariants......Page all_29622_to_00288.cpc0187.djvu
3.14. The Algebra of Covariants......Page all_29622_to_00288.cpc0188.djvu
4.2. The Geometric Quotient......Page all_29622_to_00288.cpc0189.djvu
4.4. Construction of the Quotient for an Action of a Reductive Group on an Affine Variety......Page all_29622_to_00288.cpc0191.djvu
4.5. Igusa\'s Criterion......Page all_29622_to_00288.cpc0194.djvu
4.6. Construction of the Quotient for an Action of a Reductive Group on an Arbitrary Variety......Page all_29622_to_00288.cpc0195.djvu
4.7. Homogeneous Spaces......Page all_29622_to_00288.cpc0197.djvu
4.8. Homogeneous Fiber Spaces......Page all_29622_to_00288.cpc0198.djvu
5.1. Introduction......Page all_29622_to_00288.cpc0200.djvu
5.2. Asymptotic Cones......Page all_29622_to_00288.cpc0201.djvu
5.3. The Hilbert-Mumford Criterion......Page all_29622_to_00288.cpc0202.djvu
5.4. The Support Method......Page all_29622_to_00288.cpc0203.djvu
5.5. The Characteristic of a Nilpotent Element......Page all_29622_to_00288.cpc0205.djvu
5.6. Stratification and Resolution of Singularities of the Null-Cone......Page all_29622_to_00288.cpc0209.djvu
6.1. Slices: Statement of the Problem......Page all_29622_to_00288.cpc0211.djvu
6.2. Excellent Morphisms......Page all_29622_to_00288.cpc0212.djvu
6.3. Étale Slices......Page all_29622_to_00288.cpc0213.djvu
6.4. Stabilizers of Points in a Neighborhood of a Closed Orbit......Page all_29622_to_00288.cpc0215.djvu
6.6. Étale Slices and Analytic Slices......Page all_29622_to_00288.cpc0216.djvu
6.7. Structure of Fibers of the Quotient Morphism......Page all_29622_to_00288.cpc0217.djvu
6.8. The Theorem on Reaching the Boundary of an Orbit by Means of a One-Parameter Subgroup......Page all_29622_to_00288.cpc0219.djvu
6.9. Luna\'s Stratification......Page all_29622_to_00288.cpc0220.djvu
6.10. Sheets......Page all_29622_to_00288.cpc0223.djvu
6.11. Closedness of Orbits: Luna\'s Criterion......Page all_29622_to_00288.cpc0225.djvu
6.12. Closedness of Orbits: the Kempf-Ness Criterion......Page all_29622_to_00288.cpc0226.djvu
6.13. The Closed Orbit Contained in the Closure of a Given Orbit......Page all_29622_to_00288.cpc0228.djvu
6.14. The Moment Mapping......Page all_29622_to_00288.cpc0230.djvu
7.1. Introduction......Page all_29622_to_00288.cpc0232.djvu
7.2. Existence Theorems for S.G.P......Page all_29622_to_00288.cpc0233.djvu
7.3. S.G.P. for Linear Actions......Page all_29622_to_00288.cpc0236.djvu
7.4. Closed Orbits in General Position......Page all_29622_to_00288.cpc0239.djvu
7.5. S.G.P., Chevalley Sections, and Stability......Page all_29622_to_00288.cpc0240.djvu
8.1. Good Properties in Invariant Theory......Page all_29622_to_00288.cpc0242.djvu
8.2. Inheritance of Good Properties......Page all_29622_to_00288.cpc0244.djvu
8.3. Comparison of the Algebras of Invariants of Finite and Connected Reductive Linear Groups......Page all_29622_to_00288.cpc0245.djvu
8.4. The Case of a Two-Dimensional Quotient......Page all_29622_to_00288.cpc0247.djvu
8.5. Adjoint Groups of Graded Lie Algebras (0-Groups)......Page all_29622_to_00288.cpc0248.djvu
8.6. Polar Groups......Page all_29622_to_00288.cpc0250.djvu
8.7. Enumeration of Semisimple Linear Groups with Good Properties......Page all_29622_to_00288.cpc0251.djvu
8.8. Weierstrass Sections......Page all_29622_to_00288.cpc0252.djvu
9.1. Polarization......Page all_29622_to_00288.cpc0254.djvu
9.2. Reduction of the First Fundamental Theorem......Page all_29622_to_00288.cpc0255.djvu
9.3. Invariants of Systems of Vectors and Linear Forms......Page all_29622_to_00288.cpc0257.djvu
9.4. Relations Between Invariants of Systems of Vectors and Linear Forms......Page all_29622_to_00288.cpc0258.djvu
9.5. Invariants of Tensors......Page all_29622_to_00288.cpc0260.djvu
Summary Table......Page all_29622_to_00288.cpc0263.djvu
References......Page all_29622_to_00288.cpc0267.djvu