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＜E-Book＞
Differential Galois theory through Riemann-Hilbert correspondence : an elementary introduction / Jacques Sauloy
(Graduate Studies in Mathematics ; v. 177)

Publisher	(Providence, Rhode Island : American Mathematical Society)
Year	[2016]
Size	1 online resource (pages cm.)
Authors	*Sauloy, Jacques
Subjects	LCSH:Galois theory LCSH:Riemann-Hilbert problems FREE:Field theory and polynomials -- Differential and difference algebra -- Differential algebra  All Subject Search FREE:Functions of a complex variable -- Riemann surfaces -- None of the above, but in this section  All Subject Search FREE:Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.)  All Subject Search FREE:Ordinary differential equations -- General theory -- Linear equations and systems, general  All Subject Search FREE:Ordinary differential equations -- Differential equations in the complex domain -- Differential equations in the complex domain  All Subject Search
Contents	Chapter 1. The complex exponential function Chapter 2. Power series Chapter 3. Analytic functions Chapter 4. The complex logarithm Chapter 5. From the local to the global Chapter 6. Two basic equations and their monodromy Chapter 7. Linear complex analytic differential equations Chapter 8. A functorial point of view on analytic continuation: Local systems Chapter 9. Regular singular points and the local Riemann-Hilbert correspondence Chapter 10. Local Riemann-Hilbert correspondence as an equivalence of categories Chapter 11. Hypergeometric series and equations Chapter 12. The global Riemann-Hilbert correspondence Chapter 13. Local differential Galois theory Chapter 14. The local Schlesinger density theorem Chapter 15. The universal (Fuchsian local) Galois group Chapter 16. The universal group as proalgebraic hull of the fundamental group Chapter 17. Beyond local Fuchsian differential Galois theory Appendix A. Another proof of the surjectivity of $\mathrm {exp}:\mathrm {Mat}_n(\mathbf {C})\rightarrow \mathrm {GL}_n(\mathbf {C})$ Appendix B. Another construction of the logarithm of a matrix Appendix C. Jordan decomposition in a linear algebraic group Appendix D. Tannaka duality without schemes Appendix E. Duality for diagonalizable algebraic groups Appendix F. Revision problems
Notes	Includes bibliographical references and index Access is restricted to licensed institutions Electronic reproduction Providence, Rhode Island American Mathematical Society 2016 Mode of access : World Wide Web Description based on print version record HTTP:URL=http://www.ams.org/gsm/177 Information=Contents HTTP:URL=https://doi.org/10.1090/gsm/177 Information=Contents

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