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Torsors, Reductive Group Schemes and Extended Affine Lie Algebras.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2013Copyright date: ©2013Edition: 1st edDescription: 1 online resource (124 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470410636
Subject(s): Genre/Form: Additional physical formats: Print version:: Torsors, Reductive Group Schemes and Extended Affine Lie AlgebrasDDC classification:
  • 512/.482
LOC classification:
  • QA252.3 -- .G55 2013eb
Online resources:
Contents:
Intro -- 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 -loop adjoint groups -- 8.4. Action of _{ }(ℤ) -- 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 ₂ -- Chapter 12. Case of groups of type ₄, ₈ and simply connected ₇ 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 _{ ,ℤ} -- 15.2. The general case -- Chapter 16. Appendix 2: Global automorphisms of -torsors over the projective line -- Bibliography.
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Intro -- 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 -loop adjoint groups -- 8.4. Action of _{ }(ℤ) -- 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 ₂ -- Chapter 12. Case of groups of type ₄, ₈ and simply connected ₇ 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 _{ ,ℤ} -- 15.2. The general case -- Chapter 16. Appendix 2: Global automorphisms of -torsors over the projective line -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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