Galois theory, coverings, and Riemann surfaces
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Livre numérique |
| Sprache: | Anglais |
| Veröffentlicht: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
2013.
Cham : Springer Nature |
| Schlagworte: | |
| Online Zugang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Anmerkung: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Galois theory, coverings, and Riemann surfaces, Askold Khovanskii, Berlin, Springer, 2013, 1 vol. (VIII-81 p.), 978-3-642-38840-8 • Galois Theory, Coverings, and Riemann Surfaces, Texte imprimé, 9783642388422 • Galois Theory, Coverings, and Riemann Surfaces, Texte imprimé, 9783662519561 |
Inhaltsangabe:
- Chapter 1 Galois Theory: 1.1 Action of a Solvable Group and Representability by Radicals
- 1.2 Fixed Points under an Action of a Finite Group and Its Subgroups
- 1.3 Field Automorphisms and Relations between Elements in a Field
- 1.4 Action of a k-Solvable Group and Representability by k-Radicals
- 1.5 Galois Equations
- 1.6 Automorphisms Connected with a Galois Equation
- 1.7 The Fundamental Theorem of Galois Theory
- 1.8 A Criterion for Solvability of Equations by Radicals
- 1.9 A Criterion for Solvability of Equations by k-Radicals
- 1.10 Unsolvability of Complicated Equations by Solving Simpler Equations
- 1.11 Finite Fields
- Chapter 2 Coverings: 2.1 Coverings over Topological Spaces
- 2.2 Completion of Finite Coverings over Punctured Riemann Surfaces
- Chapter 3 Ramified Coverings and Galois Theory: 3.1 Finite Ramified Coverings and Algebraic Extensions of Fields of Meromorphic Functions
- 3.2 Geometry of Galois Theory for Extensions of a Field of Meromorphic Functions
- References
- Index.