05739nam 2201345 450 991081320830332120210504020004.01-4008-7402-510.1515/9781400874026(CKB)3710000000485483(EBL)4001611(SSID)ssj0001554883(PQKBManifestationID)16179870(PQKBTitleCode)TC0001554883(PQKBWorkID)13759220(PQKB)10091768(StDuBDS)EDZ0001756490(DE-B1597)468952(OCoLC)979687281(DE-B1597)9781400874026(Au-PeEL)EBL4001611(CaPaEBR)ebr11124043(CaONFJC)MIL832712(OCoLC)932328021(MiAaPQ)EBC4001611(EXLCZ)99371000000048548320151223h20162016 uy 0engurnnu---|u||utxtccrClassification of pseudo-reductive groups /Brian Conrad, Gopal PrasadPrinceton, New Jersey ;Oxford, England :Princeton University Press,2016.©20161 online resource (256 p.)Annals of Mathematics Studies ;Number 191Description based upon print version of record.0-691-16793-1 0-691-16792-3 Includes bibliographical references and index.Front matter --Contents --1. Introduction --2. Preliminary notions --3. Field-theoretic and linear-algebraic invariants --4. Central extensions and groups locally of minimal type --5. Universal smooth k-tame central extension --6. Automorphisms, isomorphisms, and Tits classification --7. Constructions with regular degenerate quadratic forms --8. Constructions when Φ has a double bond --9. Generalization of the standard construction --A. Pseudo-isogenies --B. Clifford constructions --C. Pseudo-split and quasi-split forms --D. Basic exotic groups of type F4 of relative rank 2 --Bibliography --IndexIn the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic.Annals of mathematics studies ;Number 191.Linear algebraic groupsGroup theoryGeometry, Algebraic"ient homomorphism.Cartan k-subgroup.Dynkin diagram.Isogeny Theorem.Isomorphism Theorem.Levi subgroup.SeveriЂrauer variety.Tits classification.Tits-style classification.Weil restriction.algebraic geometry.automorphism functor.automorphism scheme.automorphism.canonical central extensions.central "ient.central extension.characteristic 2.conformal isometry.degenerate quadratic form.double bond.exotic construction.field-theoretic invariant.generalized exotic group.generalized standard group.generalized standard presentation.generalized standard.isomorphism class.isomorphism.isotropic group.k-tame central extension.linear isomorphism.linear-algebraic invariant.maximal torus.minimal type.non-reduced root system.number theory.pseudo-isogeny.pseudo-reductive group.pseudo-semisimple group.pseudo-simple group.pseudo-simple k-group.pseudo-split form.pseudo-split.quadratic space.quadrics.rank-1.rank-2.rigidity property.root field.root system.scheme-theoretic center.semisimple "ient.semisimple k-group.structure theorem.Linear algebraic groups.Group theory.Geometry, Algebraic.512/.55Conrad Brian1970-65658Prasad GopalMiAaPQMiAaPQMiAaPQBOOK9910813208303321Classification of pseudo-reductive groups4099425UNINA