Differential algebra and diophantine geometry

Title page......Page 1
Contents......Page 3
Introduction......Page 5
1. Preliminaries......Page 9
2. Geometric Hermite Theorem......Page 15
3. Geometric Chevalley-Weil Theorem......Page 17
4. Geometric Weak Mordell-Weil Theorem......Page 18
5. Geometric heights......Page 19
6. Geometric Mordell- Weil Theorem......Page 25
1. Main concepts......Page 28
2. Division Algorithm......Page 33
3. Differential Basis Theorem......Page 37
4. Differential Ellimination Theorem......Page 39
5. Differential Nullstellensatz......Page 41
6. D-modules......Page 45
7. Further results......Page 47
1. Differential regular maps of algebraic varieties......Page 50
2. Prolongations versus torsors......Page 68
3. Differential polynomial functions versus prolongations......Page 76
4. Miscellanea on differential polynomial functions......Page 90
5. Differential regular functions versus differential polynomial ones......Page 99
6. Differential tangent maps......Page 112
1. Differential regular sections of vector bundles......Page 119
2. The projective line......Page 122
3. Remarks on the differential Liiroth problem......Page 126
4. Differential density of rational points......Page 127
1. Structure of Aoo......Page 129
2. Differential character maps of abelian varieties......Page 135
3. Differential tangent maps of differential character maps......Page 138
4. Quotients of abelian varieties......Page 144
1. Differential algebraic descent method......Page 149
2. Finiteness Theorem for differential Lagrangian maps......Page 155
3. Differential algebraic analogue of Lang's conjecture......Page 160
4. Infinitesimal analogue of Lang's conjecture......Page 162
5. Differential algebraic analogue of the Isogeny Theorem......Page 164
1. Geometric Lang Conjecture......Page 171
2. Geometric Mordell Conjecture......Page 172
3. Geometric Siegel Theorem......Page 176
Appendix: Big Picard......Page 178
References......Page 183
Index of terminology......Page 187
Index of notations......Page 190