Notes on the Witt Classification of Hermitian Innerproduct Spaces over a Ring of Algebraic Integers
The lectures comprising this volume were delivered by P. E. Conner 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.
1000841667
Notes on the Witt Classification of Hermitian Innerproduct Spaces over a Ring of Algebraic Integers
The lectures comprising this volume were delivered by P. E. Conner 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.
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Notes on the Witt Classification of Hermitian Innerproduct Spaces over a Ring of Algebraic Integers

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

by P. E. Conner Jr.
Notes on the Witt Classification of Hermitian Innerproduct Spaces over a Ring of Algebraic Integers

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

by P. E. Conner Jr.

Overview

The lectures comprising this volume were delivered by P. E. Conner 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.

Product Details

ISBN-13: 9780292740679
Publisher: University of Texas Press
Publication date: 08/01/1979
Pages: 158
Product dimensions: 8.50(w) x 11.00(h) x 0.34(d)

About the Author

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

Table of Contents

  • 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
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Related Subjects

Science & Technology
Mathematics
Geometry
Algebra
Geometry - Euclidean & Projective
Mathematical Rings
Mathematical Spaces
Mathematics - Fields
Vectors & Tensors
Science & Technology
Mathematics
Geometry
Algebra
Geometry - Euclidean & Projective
Mathematical Rings
Mathematical Spaces
Mathematics - Fields
Vectors & Tensors

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