Author | Waterhouse, William C. author |
---|---|
Title | Introduction to Affine Group Schemes [electronic resource] / by William C. Waterhouse |
Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6217-6 |
Descript | XII, 164 p. online resource |
I The Basic Subject Matter -- 1 Affine Group Schemes -- 2 Affine Group Schemes: Examples -- 3 Representations -- 4 Algebraic Matrix Groups -- II Decomposition Theorems -- 5 Irreducible and Connected Components -- 6 Connected Components and Separable Algebras -- 7 Groups of Multiplicative Type -- 8 Unipotent Groups -- 9 Jordan Decomposition -- 10 Nilpotent and Solvable Groups -- III The Infinitesimal Theory -- 11 Differentials -- 12 Lie Algebras -- IV Faithful Flatness and Quotients -- 13 Faithful Flatness -- 14 Faithful Flatness of Hopf Algebras -- 15 Quotient Maps -- 16 Construction of Quotients -- V Descent Theory -- 17 Descent Theory Formalism -- 18 Descent Theory Computations -- Appendix: Subsidiary Information -- A.1 Directed Sets and Limits -- A.2 Exterior Powers -- A.3 Localization. Primes, and Nilpotents -- A.4 Noetherian Rings -- A.5 The Hilbert Basis Theorem -- A.6 The Krull Intersection Theorem -- A.7 The Nocthcr Normalization Lemma -- A.8 The Hilbert Nullstellensatz -- A.9 Separably Generated Fields -- A.10 Rudimentary Topological Terminology -- Further Reading -- Index of Symbols