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035   $a(DE-B1597)9781400874026
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100   $a20151223h20162016  uy             0
101 0 $aeng
135   $aurnnu---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aClassification of pseudo-reductive groups /$fBrian Conrad, Gopal Prasad
210  1$aPrinceton, New Jersey ;$aOxford, England :$cPrinceton University Press,$d2016.
210  4$dİ2016
215   $a1 online resource (256 p.)
225 1 $aAnnals of Mathematics Studies ;$vNumber 191
300   $aDescription based upon print version of record.
311   $a0-691-16793-1 
311   $a0-691-16792-3 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$t1. Introduction --$t2. Preliminary notions --$t3. Field-theoretic and linear-algebraic invariants --$t4. Central extensions and groups locally of minimal type --$t5. Universal smooth k-tame central extension --$t6. Automorphisms, isomorphisms, and Tits classification --$t7. Constructions with regular degenerate quadratic forms --$t8. Constructions when ? has a double bond --$t9. Generalization of the standard construction --$tA. Pseudo-isogenies --$tB. Clifford constructions --$tC. Pseudo-split and quasi-split forms --$tD. Basic exotic groups of type F4 of relative rank 2 --$tBibliography --$tIndex
330   $aIn the earlier monograph Pseudo-reductive Groups, Brian Conrad, Ofer Gabber, and Gopal Prasad explored the general structure of pseudo-reductive groups. In this new book, Classification of Pseudo-reductive Groups, Conrad and Prasad go further to study the classification over an arbitrary field. An isomorphism theorem proved here determines the automorphism schemes of these groups. The book also gives a Tits-Witt type classification of isotropic groups and displays a cohomological obstruction to the existence of pseudo-split forms. Constructions based on regular degenerate quadratic forms and new techniques with central extensions provide insight into new phenomena in characteristic 2, which also leads to simplifications of the earlier work. A generalized standard construction is shown to account for all possibilities up to mild central extensions. The results and methods developed in Classification of Pseudo-reductive Groups will interest mathematicians and graduate students who work with algebraic groups in number theory and algebraic geometry in positive characteristic.
410  0$aAnnals of mathematics studies ;$vNumber 191.
606   $aLinear algebraic groups
606   $aGroup theory
606   $aGeometry, Algebraic
610   $a"ient homomorphism.
610   $aCartan k-subgroup.
610   $aDynkin diagram.
610   $aIsogeny Theorem.
610   $aIsomorphism Theorem.
610   $aLevi subgroup.
610   $aSeveri?rauer variety.
610   $aTits classification.
610   $aTits-style classification.
610   $aWeil restriction.
610   $aalgebraic geometry.
610   $aautomorphism functor.
610   $aautomorphism scheme.
610   $aautomorphism.
610   $acanonical central extensions.
610   $acentral "ient.
610   $acentral extension.
610   $acharacteristic 2.
610   $aconformal isometry.
610   $adegenerate quadratic form.
610   $adouble bond.
610   $aexotic construction.
610   $afield-theoretic invariant.
610   $ageneralized exotic group.
610   $ageneralized standard group.
610   $ageneralized standard presentation.
610   $ageneralized standard.
610   $aisomorphism class.
610   $aisomorphism.
610   $aisotropic group.
610   $ak-tame central extension.
610   $alinear isomorphism.
610   $alinear-algebraic invariant.
610   $amaximal torus.
610   $aminimal type.
610   $anon-reduced root system.
610   $anumber theory.
610   $apseudo-isogeny.
610   $apseudo-reductive group.
610   $apseudo-semisimple group.
610   $apseudo-simple group.
610   $apseudo-simple k-group.
610   $apseudo-split form.
610   $apseudo-split.
610   $aquadratic space.
610   $aquadrics.
610   $arank-1.
610   $arank-2.
610   $arigidity property.
610   $aroot field.
610   $aroot system.
610   $ascheme-theoretic center.
610   $asemisimple "ient.
610   $asemisimple k-group.
610   $astructure theorem.
615  0$aLinear algebraic groups.
615  0$aGroup theory.
615  0$aGeometry, Algebraic.
676   $a512/.55
700   $aConrad$b Brian$f1970-$065658
702   $aPrasad$b Gopal
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910797511403321
996   $aClassification of pseudo-reductive groups$93689928
997   $aUNINA