Notes on the Witt Classification of Hermitian Innerproduct Spaces Over a Ring of Algebraic Integers

P. E. Conner was Nicholson Professor of Mathematics at Louisiana State University.

• Introduction I. Relative Quadratic Extensions 1. Extension of primes 2. Hilbert symbols 3. The group Gen(E/F) 4. The group Iso(E/F) 5. The unramified case 6. Examples II. The Witt Ring H(E) 1. General definitions 2. Anisotropic representatives 3. Invariants for H(E) 4. Algebraic number fields III. Torsion Forms 1. Torsion OE-modules 2. The quotient E/K 3. Torsion innerproducts 4. Localizers 5. The inverse different IV. The Group Hu(K) 1. Basic definitions 2. The group Iso(E/F) again 3. The Knebusch exact sequence 4. Localization 5. Computing Hu(K) 6. The ring H(OE) 7. The Cokernel of Δ V. The Witt Ring W(OF) 1. Symbols 2. The boundary operator 3. The ring W(OF) References Symbol List