Quadratic and Hermitian Forms over Rings

摘要: I. Hermitian Forms over Rings.- 1. Rings with Involution.- 2. Sesquilinear and Forms.- 3. Modules.- 4. Symplectic Spaces.- 5. Unitary 6. Spaces Division 7. Change of 8. Products 9. Morita Theory for 10. Witt Groups.- 11. Cartesian Diagrams Patching II. in Categories.- Additive Categories Duality.- Transfer.- Reduction.- The Theorem Krull-Schmidt Some Applications.- III. Descent Cohomology.- Elements.- Modules Algebras.- Discriminant Quadratic Azumaya Graded Algebras Universal Norms.- Involutions on Pfaffian.- IV. Clifford Algebra.- Construction the Structure Algebra, Even Rank Case.- Odd Arf Invariant.- Special Orthogonal Group.- Spinors.- Canonical Isomorphisms.- Invariants Trivial V. Low Rank.- 1.- 2.- 3.- 4.- 5 6.- Composition VI. Splitting Cancellation Theorems.- Semilocal Rings, Stable Range.- f-Rank.- Serre's Cancellation.- Stability A Theorem.- VII. Polynomial Principal Ideal Domains.- Bundles $$\mathbb{P}^1_D$$.- Karoubi.- Quillen's Rigidity Horrocks Isotropic Projective Indecomposable Anisotropic VIII. Groups Affine Group Schemes.- Domains Dimension ?3.- Regular Local Essentially Finite Type.- Real Smooth Surfaces.- Curves.- Examples.- Surfaces.