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