Notes on the Witt Classification of Hermitian Innerproduct Spaces over a Ring of Algebraic Integers [Paperback]

The lectures comprising this volume were delivered by P. E. Conner, Nicholson Professor of Mathematics at Louisiana State University, at the University of Texas at Austin in 1978. The lectures are intended to give mathematicians at the graduate level and beyond some powerful algebraic and number theoretical tools for formulating and solving certain types of classification problems in topology.

• 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