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The Second Chinburg Conjecture for Quaternion Fields
Jeff Hooper, University of Durham, UK, Victor Snaith, University of Southhampton, Southampton, UK, and Minh van Tran, A C Nielsen Vietnam--Tecasin Business Centre, Ho Chi Minh City, Vietnam
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Memoirs of the American Mathematical Society
2000; 133 pp; softcover
Volume: 148
ISBN-10: 0-8218-2164-4
ISBN-13: 978-0-8218-2164-0
List Price: US$50
Individual Members: US$30
Institutional Members: US$40
Order Code: MEMO/148/704
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The Second Chinburg Conjecture relates the Galois module structure of rings of integers in number fields to the values of the Artin root number on the symplectic representations of the Galois group. We establish the Second Chinburg Conjecture for all quaternion fields.

Readership

Graduate students and research mathematicians interested in number theory, algebra, and algebraic \(K\)-theory.

Table of Contents

  • Introduction
  • Class-groups of group-rings
  • The evaluation of \([X]\)
  • Quaternion fields over \(\mathbf{Q}_2\)
  • The invariant in Cases A, B and C
  • The evaluation of \([M]\)
  • The conjecture in Cases A, B and C
  • Epilogue
  • Bibliography
  • Index
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