Date of Award
Doctor of Philosophy (PhD)
Professor V.P. Snaith
This thesis is a part of a program to study the Second Chinburg Conjecture. Let N be a quaternion extension of the rational; containing Q(√d₁,√d₂), where d₁ ≡ 3 (mod 8) and d₂ ≡ 10 (mod 16). A projective Z[Q₈]-module inside the ring of integers ON is constructed and is used, together with a cohomological classification of cohomologically trivial, 2-primary Q-modules, to compare Ω(N/Q,2), Chinburg's second invariant, with WN/Q, the root number class defined by Ph. Cassou-Nougès and A. Fröhlich. The Second Chinburg Conjecture for this extension N/Q is confirmed. Together with results of J. Hooper and S. Kim this calculation verifies the Second Chinburg Conjecture for all quaternion extensions of the rationals.
Tran, Minh Van, "The Second Chinburg Conjecture for Quaternion Fields" (1996). Open Access Dissertations and Theses. Paper 2429.