Unipotent Algebraic Groups |
Contents
Introduction | 1 |
Forms of vector groups groups of Russell type 17 | 17 |
3 Decomposition theorems for central extensions | 29 |
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abelian affine algebraic affine k-group scheme affine k-scheme algebraic closure algebraic group arithmetic genus assume biadditive canonical central extension closed subgroup coaction cohomology commutative k-group scheme Comod comodule COROLLARY defined denote DG-III DG-IV divisor divisor class group exact sequence Ext cent faithfully flat finite dimensional functor G₁ G₂ ground field Hence Homk F Homk-gr homomorphism Hopf algebra hy G induced integer invertible sheaf isomorphic k-algebra k-closed k-derivation k-form k-G-module k-group of Russell k-group scheme k-homomorphism k-isomorphic k-module k-morphism k-normal completion k-rational point k-smooth k-wound k[F]-module k[t₁ left k F]-module LEMMA Let G M₁ M₂ module morphism nonconstant notations one-dimensional unipotent Picc/k polynomial ring Proof purely inseparable quotient Russell type Spec structure subgroup scheme Suppose surjective Theorem two-dimensional unipotent unipotent algebraic group unipotent k-group unique unique factorization domain vector group