Classification of Pseudo-reductive Groups
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A01=Brian Conrad
A01=Gopal Prasad
Absolute Galois group
Adjoint
Affine group
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Author_Brian Conrad
Author_Gopal Prasad
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Automorphism
Bijection
Bruhat decomposition
Calculation
Cartan subgroup
Category1=Non-Fiction
Category=PBF
Centrality
Classification theorem
Clifford algebra
Commutative diagram
Commutative property
Commutator
Compactification (mathematics)
Composition series
COP=United States
Coset
Counterexample
Degenerate bilinear form
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Diagram (category theory)
Direct product
Discrete valuation ring
Dynkin diagram
Elementary proof
eq_isMigrated=2
eq_nobargain
Existential quantification
Factorization
Finite set
Functor
Galois extension
Galois theory
Ground field
Group scheme
Homomorphism
Hyperbolic geometry
Identity component
Injective function
Isogeny
Isomorphism class
Isomorphism theorem
K-group
Language_English
Lie algebra
Linear algebra
Linear algebraic group
Linear map
Local ring
Maximal torus
Natural transformation
Normal subgroup
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Pointed set
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Pseudo-reductive group
Purely inseparable extension
Pushout (category theory)
Quadratic form
Quadratic residue
Quadric
Reductive group
Residue field
Ring extension
Root system
Separable extension
Smoothness
softlaunch
Special case
Subgroup
Summation
Surjective function
Theorem
Tuple
Universal property
Weil restriction
Weyl group
Product details
- ISBN 9780691167923
- Weight: 482g
- Dimensions: 152 x 235mm
- Publication Date: 10 Nov 2015
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
- Language: English
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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.
Brian Conrad is professor of mathematics at Stanford University. Gopal Prasad is the Raoul Bott Professor of Mathematics at the University of Michigan.
