Galois Theory of Linear Differential Equations

Cover......Page 1 ISBN......Page 5 Preface......Page 8 Contents......Page 16 Algebraic Theory......Page 22 1 Picard-Vessiot Theory......Page 24 2 Differential Operators and Differential Modules......Page 60 3 Formal Local Theory......Page 84 4 Algorithmic Considerations......Page 126 Analytic Theory......Page 168 5 Monodromy, the Riemann-Hilbert Problem and the Differential Galois Group......Page 170 6 Differential Euqations on the Complex Sphere anf the Riemann-Hilbert Problem......Page 184 7 Exact Asymptotics......Page 214 8 Stokes Phenomenon and Differential Galois Groups......Page 258 9 Stokes Matrices and Meromorphic Classification......Page 274 10 Universal Picard-Vessiot Rings and Galois Groups......Page 290 11 Inverse Problems......Page 302 12 Moduli for Singular Differential Equations......Page 326 13 Positive Characteristic......Page 348 Appendices......Page 368 A Algebraic Geometry......Page 370 B Tannakian Categories......Page 406 C Sheaves and Cohomology......Page 424 D Partial Differential Equations......Page 444 Bibliography......Page 454 List of Notations......Page 476 Index......Page 479 Back cover......Page 484