| Description |
1 online resource |
| Series |
Memoirs of the American Mathematical Society ; v. 226 |
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Memoirs of the American Mathematical Society.
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| Contents |
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 |
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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 |
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""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"" |
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""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"" |
| Notes |
Title from content provider |
| Subject |
Kac-Moody algebras.
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Linear algebraic groups.
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Geometry, Algebraic.
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Geometry, Algebraic
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Kac-Moody algebras
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Linear algebraic groups
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| Form |
Electronic book
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| Author |
Pianzola, Arturo
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| ISBN |
9781470410636 |
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147041063X |
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