Torsors, reductive group schemes and extended affine lie algebras /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Gille, Philippe
Otros Autores: Pianzola, Arturo
Formato: Electrónico eBook
Idioma:Inglés
Publicado: [Place of publication not identified] : [publisher not identified]
Colección:Memoirs of the American Mathematical Society.
Temas:
Kac-Moody algebras.
Linear algebraic groups.
Geometry, Algebraic.
Algèbres de Kac-Moody.
Groupes linéaires algébriques.
Géométrie algébrique.
Geometry, Algebraic
Kac-Moody algebras
Linear algebraic groups
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Chapter 1. Introduction
  • Chapter 2. Generalities on the algebraic fundamental group, torsors, and reductive group schemes
  • 2.1. The fundamental group
  • 2.2. Torsors
  • 2.3. An example: Laurent polynomials in characteristic 0
  • 2.4. Reductive group schemes: Irreducibility and isotropy
  • Chapter 3. Loop, finite and toral torsors
  • 3.1. Loop torsors
  • 3.2. Loop reductive groups
  • 3.3. Loop torsors at a rational base point
  • 3.4. Finite torsors
  • 3.5. Toral torsors
  • Chapter 4. Semilinear considerations
  • 4.1. Semilinear morphisms
  • 4.2. Semilinear morphisms4.3. Case of affine schemes
  • 4.4. Group functors
  • 4.5. Semilinear version of a theorem of Borel-Mostow
  • 4.6. Existence of maximal tori in loop groups
  • 4.7. Variations of a result of Sansuc
  • Chapter 5. Maximal tori of group schemes over the punctured line
  • 5.1. Twin buildings
  • 5.2. Proof of Theorem 5.1
  • Chapter 6. Internal characterization of loop torsors and applications
  • 6.1. Internal characterization of loop torsors
  • 6.2. Applications to (algebraic) Laurent series
  • Chapter 7. Isotropy of loop torsors
  • ""7.1. Fixed point statements""""7.2. Case of flag varieties""; ""7.3. Anisotropic loop torsors""; ""Chapter 8. Acyclicity""; ""8.1. The proof""; ""8.2. Application: Witt-Tits decomposition""; ""8.3. Classification of semisimple â€?loop adjoint groups""; ""8.4. Action of _{ }(â??)""; ""Chapter 9. Small dimensions""; ""9.1. The one-dimensional case""; ""9.2. The two-dimensional case""; ""Chapter 10. The case of orthogonal groups""; ""Chapter 11. Groups of type â??""; ""Chapter 12. Case of groups of type â??, â?? and simply connected â?? in nullity 3""
  • ""Chapter 13. The case of _{ }""""13.1. Loop Azumaya algebras""; ""13.2. The one-dimensional case""; ""13.3. The geometric case""; ""13.4. Loop algebras of inner type ""; ""Chapter 14. Invariants attached to EALAs and multiloop algebras""; ""Chapter 15. Appendix 1: Pseudo-parabolic subgroup schemes""; ""15.1. The case of _{, â??}""; ""15.2. The general case""; ""Chapter 16. Appendix 2: Global automorphisms of â€?torsors over the projective line""; ""Bibliography""

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