دانلود کتاب Classification of Pseudo-reductive Groups (AM-191)

فهرست مطالب :

Cover\nTitle\nCopyright\nContents\n1 Introduction\n 1.1 Motivation\n 1.2 Root systems and new results\n 1.3 Exotic groups and degenerate quadratic forms\n 1.4 Tame central extensions\n 1.5 Generalized standard groups\n 1.6 Minimal type and general structure theorem\n 1.7 Galois-twisted forms and Tits classification\n 1.8 Background, notation, and acknowledgments\n2 Preliminary notions\n 2.1 Standard groups, Levi subgroups, and root systems\n 2.2 The basic exotic construction\n 2.3 Minimal type\n3 Field-theoretic and linear-algebraic invariants\n 3.1 A non-standard rank-1 construction\n 3.2 Minimal field of definition for Ru(Gk̅)\n 3.3 Root field and applications\n 3.4 Application to classification results\n4 Central extensions and groups locally of minimal type\n 4.1 Central quotients\n 4.2 Beyond the quadratic case\n 4.3 Groups locally of minimal type\n5 Universal smooth k-tame central extension\n 5.1 Construction of central extensions\n 5.2 A universal construction\n 5.3 Properties and applications of G̃\n6 Automorphisms, isomorphisms, and Tits classification\n 6.1 Isomorphism Theorem\n 6.2 Automorphism schemes\n 6.3 Tits-style classification\n7 Constructions with regular degenerate quadratic forms\n 7.1 Regular degenerate quadratic forms\n 7.2 Conformal isometries\n 7.3 Severi–Brauer varieties\n8 Constructions when Φ has a double bond\n 8.1 Additional constructions for type B\n 8.2 Constructions for type C\n 8.3 Exceptional construction for rank 2\n 8.4 Generalized exotic groups\n 8.5 Structure of ZG and ZG,C\n9 Generalization of the standard construction\n 9.1 Generalized standard groups\n 9.2 Structure theorem\nA Pseudo-isogenies\n A.1 Main result\n A.2 Proof of Pseudo-Isogeny Theorem\n A.3 Relation with the semisimple case\nB Clifford constructions\n B.1 Type B\n B.2 Type C\n B.3 Cases with [k : k^2] ≤ 8\n B.4 Type BC\nC Pseudo-split and quasi-split forms\n C.1 General characteristic\n C.2 Quasi-split forms\n C.3 Rank-1 cases\n C.4 Higher-rank and non-reduced cases\nD Basic exotic groups of type F4 of relative rank 2\n D.1 General preparations\n D.2 Forms of k-rank 2\nBibliography\nIndex