作者 Sauloy, Jacques
書名 Differential Galois theory through Riemann-Hilbert correspondence : [electronic resource] an elementary introduction / Jacques Sauloy
出版項 Providence, Rhode Island : American Mathematical Society, [2016]
國際標準書號 9781470435936 (online)
book jacket
說明 1 online resource (pages cm.)
text txt rdacontent
unmediated n rdamedia
volume nc rdacarrier
系列 Graduate Studies in Mathematics, v. 177
附註 Includes bibliographical references and index
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
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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2016
Mode of access : World Wide Web
Description based on print version record
鏈接 Print version: Sauloy, Jacques. Differential Galois theory through Riemann-Hilbert correspondence : (DLC) 2016033241 1065-7339 9781470430955
主題 Galois theory
Riemann-Hilbert problems
Field theory and polynomials -- Differential and difference algebra -- Differential algebra. msc
Functions of a complex variable -- Riemann surfaces -- None of the above, but in this section. msc
Ordinary differential equations -- Instructional exposition (textbooks, tutorial papers, etc.). msc
Ordinary differential equations -- General theory -- Linear equations and systems, general. msc
Ordinary differential equations -- Differential equations in the complex domain -- Differential equations in the complex domain. msc