Author | Knus, Max-Albert. author |
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Title | Quadratic and Hermitian Forms over Rings [electronic resource] / by Max-Albert Knus |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1991 |
Connect to | http://dx.doi.org/10.1007/978-3-642-75401-2 |
Descript | XI, 524 p. online resource |
I. Hermitian Forms over Rings -- ยง1. Rings with Involution -- ยง2. Sesquilinear and Hermitian Forms -- ยง3. Hermitian Modules -- ยง4. Symplectic Spaces -- ยง5. Unitary Rings and Modules -- ยง6. Hermitian Spaces over Division Rings -- ยง7. Change of Rings -- ยง8. Products of Hermitian Forms -- ยง9. Morita Theory for Hermitian Modules -- ยง10. Witt Groups -- ยง11. Cartesian Diagrams and Patching of Hermitian Forms -- II. Forms in Categories -- ยง1. Additive Categories -- ยง2. Categories with Duality -- ยง3. Transfer -- ยง4. Reduction -- ยง5. The Theorem of Krull-Schmidt for Additive Categories -- ยง6. The Krull-Schmidt Theorem for Hermitian Spaces -- ยง7. Some Applications -- III. Descent Theory and Cohomology -- ยง1. Descent of Elements -- ยง2. Descent of Modules and Algebras -- ยง3. Discriminant Modules -- ยง4. Quadratic Algebras -- ยง5. Azumaya Algebras -- ยง6. Graded Algebras and Modules -- ยง7. Universal Norms -- ยง8. Involutions on Azumaya Algebras -- ยง9. The Pfaffian -- IV. The Clifford Algebra -- ยง1. Construction of the Clifford Algebra -- ยง2. Structure of the Clifford Algebra, the Even Rank Case -- ยง3. Structure of the Clifford Algebra, the Odd Rank Case -- ยง4. The Discriminant and the Arf Invariant -- ยง5. The Special Orthogonal Group -- ยง6. The Spinors -- ยง7. Canonical Isomorphisms -- ยง8. Invariants of Quadratic Spaces -- ยง9. Quadratic Spaces with Trivial Arf Invariant -- V. Forms of Low Rank -- ยง1. Quadratic Modules of Rank 1 -- ยง2. Quadratic Modules of Rank 2 -- ยง3. Quadratic Modules of Rank 3 -- ยง4. Quadratic Modules of Rank 4 -- ยง5. Quadratic Spaces of Rank 5 and 6 -- ยง6. Hermitian Modules of Low Rank -- ยง7. Composition of Quadratic Spaces -- VI. Splitting and Cancellation Theorems -- ยง1. Semilocal Rings, the Stable Range -- ยง2. The f-Rank -- ยง3. Serreโs Splitting Theorem and Cancellation -- ยง4. Unitary Groups -- ยง5. Cancellation for Unitary Spaces over Semilocal Rings -- ยง6. Cancellation and Stability for Unitary Spaces -- ยง7. A Splitting Theorem -- VII. Polynomial Rings -- ยง1. Principal Ideal Domains -- ยง2. Polynomial Rings -- ยง3. Bundles over $$\mathbb{P}̂1_D$$ -- ยง4. The Theorem of Karoubi -- ยง5. Quillenโs Theorem -- ยง6. A Rigidity Theorem and the Horrocks Theorem -- ยง7. Isotropic Hermitian Spaces -- ยง8. Projective Modules over Polynomial Rings -- ยง9. Hermitian Spaces of Low Rank -- ยง10. Indecomposable Anisotropic Spaces -- ยง11. Hermitian Modules over Projective Spaces -- VIII. Witt Groups of Affine Rings -- ยง1. Witt Group of Schemes -- ยง2. Domains of Dimension ?3 -- ยง3. Regular Local Rings Essentially of Finite Type -- ยง4. Real Smooth Surfaces -- ยง5. Real Curves -- ยง6. Examples -- ยง7. Symplectic Bundles over Affine Surfaces