Table of Contents

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.