Introduction to Affine Group Schemes [1 ed.] 0387904212, 9780387904214
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276 86 3MB
English Pages 164 [174] Year 1979
Table of contents :
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Affine Group Schemes....Pages 3-12
Affine Group Schemes: Examples....Pages 13-20
Representations....Pages 21-27
Algebraic Matrix Groups....Pages 28-35
Front Matter....Pages 37-37
Irreducible and Connected Components....Pages 39-45
Connected Components and Separable Algebras....Pages 46-53
Groups of Multiplicative Type....Pages 54-61
Unipotent Groups....Pages 62-67
Jordan Decomposition....Pages 68-72
Nilpotent and Solvable Groups....Pages 73-79
Front Matter....Pages 81-81
Differentials....Pages 83-91
Lie Algebras....Pages 92-100
Front Matter....Pages 101-101
Faithful Flatness....Pages 103-108
Faithful Flatness of Hopf Algebras....Pages 109-113
Quotient Maps....Pages 114-120
Construction of Quotients....Pages 121-127
Front Matter....Pages 129-129
Descent Theory Formalism....Pages 131-139
Descent Theory Computations....Pages 140-150
Back Matter....Pages 151-164
Front Matter....Pages i-xi
Front Matter....Pages 1-1
Affine Group Schemes....Pages 3-12
Affine Group Schemes: Examples....Pages 13-20
Representations....Pages 21-27
Algebraic Matrix Groups....Pages 28-35
Front Matter....Pages 37-37
Irreducible and Connected Components....Pages 39-45
Connected Components and Separable Algebras....Pages 46-53
Groups of Multiplicative Type....Pages 54-61
Unipotent Groups....Pages 62-67
Jordan Decomposition....Pages 68-72
Nilpotent and Solvable Groups....Pages 73-79
Front Matter....Pages 81-81
Differentials....Pages 83-91
Lie Algebras....Pages 92-100
Front Matter....Pages 101-101
Faithful Flatness....Pages 103-108
Faithful Flatness of Hopf Algebras....Pages 109-113
Quotient Maps....Pages 114-120
Construction of Quotients....Pages 121-127
Front Matter....Pages 129-129
Descent Theory Formalism....Pages 131-139
Descent Theory Computations....Pages 140-150
Back Matter....Pages 151-164
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