LEADER 04171nam 2200613 450 001 9910480392803321 005 20170822144401.0 010 $a1-4704-1063-X 035 $a(CKB)3780000000000327 035 $a(EBL)3114045 035 $a(SSID)ssj0001034809 035 $a(PQKBManifestationID)11562942 035 $a(PQKBTitleCode)TC0001034809 035 $a(PQKBWorkID)11015565 035 $a(PQKB)11443135 035 $a(MiAaPQ)EBC3114045 035 $a(PPN)195408470 035 $a(EXLCZ)993780000000000327 100 $a20150415h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTorsors, reductive group schemes and extended affine lie algebras /$fPhilippe Gille, Arturo Pianzola 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2013. 210 4$dİ2013 215 $a1 online resource (124 p.) 225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vVolume 226, Number 1063 300 $a"Volume 226, Number 1063 (fourth of 5 numbers)." 311 $a0-8218-8774-2 320 $aIncludes bibliographical references. 327 $a""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"" 327 $a""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"" 327 $a""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 a???loop adjoint groups""; ""8.4. Action of _{ }(a???)""; ""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 a???""; ""Chapter 12. Case of groups of type a???, a??? and simply connected a??? in nullity 3"" 327 $a""Chapter 13. The case of _{ }""""13.1. Loop Azumaya algebras""; ""13.2. The one-dimensional case""; ""13.3. The geometric case""; ""13.4. Loop algebras of inner type ""; ""Chapter 14. Invariants attached to EALAs and multiloop algebras""; ""Chapter 15. Appendix 1: Pseudo-parabolic subgroup schemes""; ""15.1. The case of _{ ,a???}""; ""15.2. The general case""; ""Chapter 16. Appendix 2: Global automorphisms of a???torsors over the projective line""; ""Bibliography"" 410 0$aMemoirs of the American Mathematical Society ;$vVolume 226, Number 1063. 606 $aKac-Moody algebras 606 $aLinear algebraic groups 606 $aGeometry, Algebraic 608 $aElectronic books. 615 0$aKac-Moody algebras. 615 0$aLinear algebraic groups. 615 0$aGeometry, Algebraic. 676 $a512/.482 700 $aGille$b Philippe$f1968-$0938069 702 $aPianzola$b Arturo$f1955- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480392803321 996 $aTorsors, reductive group schemes and extended affine lie algebras$92113240 997 $aUNINA