Classification of Pseudo-reductive Groups (eBook)

Brian Conrad, Gopal Prasad (Autoren)

eBook Download: PDF | EPUB

2015
256 Seiten
Princeton University Press (Verlag)
978-1-4008-7402-6 (ISBN)

Infos

Brian Conrad is professor of mathematics at Stanford University. Gopal Prasad is the Raoul Bott Professor of Mathematics at the University of Michigan.

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In 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.

Produkt-Details

• Erscheint lt. Verlag: 10.11.2015
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Verlagsort: Princeton
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: Absolute Galois Group • Addition • Adjoint • affine group • Algebraically closed field • Algebraic Geometry • automorphism • automorphism functor • automorphism scheme • bijection • Bruhat decomposition • Calculation • canonical central extensions • Cartan k-subgroup • Cartan subgroup • Cartesian Product • central extension • Centrality • central quotient • characteristic 2 • Classification theorem • Clifford Algebra • Codimension • Commutative diagram • commutative property • commutator • Commutator subgroup • Compactification (mathematics) • composition series • conformal isometry • Connected space • corollary • Coset • counterexample • Degenerate bilinear form • degenerate quadratic form • Diagram (category theory) • direct product • Discrete valuation ring • Disjoint union • Double bond • Dynkin diagram • Elementary proof • empty set • existential quantification • exotic construction • Factorization • field-theoretic invariant • finite field • Finite set • functor • Galois extension • Galois group • Galois Theory • generalized exotic group • generalized standard • generalized standard group • generalized standard presentation • Ground field • group scheme • Homomorphism • Hyperbolic Geometry • Identity component • Injective function • Irreducible component • isogeny • Isogeny Theorem • isomorphism • isomorphism class • Isomorphism Theorem • isotropic group • K-group • k-tame central extension • Levi subgroup • Lie algebra • linear algebra • Linear algebraic group • linear-algebraic invariant • linear isomorphism • Linear map • Local ring • maximal torus • minimal type • Natural transformation • non-reduced root system • normal subgroup • Null vector • Number Theory • Numerical Integration • ORDER BY • Pointed set • projective space • pseudo-isogeny • pseudo-reductive group • pseudo-semisimple group • pseudo-simple group • pseudo-simple k-group • pseudo-split • pseudo-split form • Purely inseparable extension • Pushout (category theory) • quadratic form • Quadratic residue • quadratic space • Quadric • quadrics • quotient homomorphism • Quotient space (topology) • rank-1 • rank-2 • Rational point • reductive group • Requirement • residue field • rigidity property • Ring Extension • Root datum • root field • root system • scheme-theoretic center • scientific notation • semisimple k-group • semisimple quotient • Separable extension • SeveriЂrauer variety • Smoothness • Special case • splitting field • Structure Theorem • SUBGROUP • Subset • Summation • sum of squares • Surjective function • Tautology (logic) • Theorem • Tits classification • Tits-style classification • Triviality (mathematics) • Tuple • Universal property • Vector group • Vector Space • Weil restriction • Weyl Group • Without loss of generality
• ISBN-10: 1-4008-7402-5 / 1400874025
• ISBN-13: 978-1-4008-7402-6 / 9781400874026