Galois theory of linear differential equations/
Marius van der Put and Michael F. Singer
- Berlin: Springer, 2003.
- xvii, 438 p. : ill. ; 24 cm.
- (Grundlehren der mathematischen Wissenschaften), 328 .
Algebraic Theory -- 1. Picard-Vessiot Theory -- 2. Differential Operators and Differential Modules -- 3. Formal Local Theory -- 4. Algorithmic Considerations -- Analytic Theory -- 5. Monodromy, the Riemann-Hilbert Problem, and the Differential Galois Group -- 6. Differential Equations on the Complex Sphere and the Riemann-Hilbert Problem -- 7. Exact Asymptotics -- 8. Stokes Phenomenon and Differential Galois Groups -- 9. Stokes Matrices and Meromorphic Classification -- 10. Universal Picard-Vessiot Rings and Galois Groups -- 11. Inverse Problems -- 12. Moduli for Singular Differential Equations -- 13. Positive Characteristic -- A. Algebraic Geometry -- B. Tannakian Categories -- C. Sheaves and Cohomology -- D. Partial Differential Equations.