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