Torsors, reductive group schemes and extended affine lie algebras / / Philippe Gille, Arturo Pianzola

• Autore: Gille Philippe <1968->
• Pubblicazione: Providence, Rhode Island : , : American Mathematical Society, , 2013; ©2013
• Descrizione fisica: 1 online resource (124 p.)
• Disciplina: 512/.482
• Soggetto topico: Kac-Moody algebras; Linear algebraic groups; Geometry, Algebraic
• Soggetto genere / forma: Electronic books.
• Persona (resp. second.): PianzolaArturo <1955->
• Note generali: "Volume 226, Number 1063 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""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 morphisms""""4.3. 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""
• Titolo autorizzato: Torsors, reductive group schemes and extended affine lie algebras
• ISBN: 1-4704-1063-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910480392803321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society ; ; Volume 226, Number 1063.