Reid, Alan2022-09-262022-052022-04-21May 2022Rouse, Nicholas. "On a conjecture of Chinburg-Reid-Stover." (2022) Diss., Rice University. <a href="https://hdl.handle.net/1911/113367">https://hdl.handle.net/1911/113367</a>.https://hdl.handle.net/1911/113367EMBARGO NOTE: This item is embargoed until 2028-05-01We study a conjecture of Chinburg-Reid-Stover about ramification sets of quaternion algebras associated to hyperbolic 3-orbifolds obtained by (d,0) Dehn surgery on hyperbolic knot complements in S^3. For a sporadic example and an infinite family, we prove that the set of rational primes p such that there is some d such that the quaternion algebra associated to the (d,0) surgery is ramified at some prime ideal above p is infinite. This behavior is governed by the Alexander polynomial of the knot, and we investigate its connection to reducible representations on the canonical component of the character variety and the failure of a certain function field quaternion algebra to extend to an Azumaya algebra over the canonical component. We further provide a more general framework for finding such examples that one may use to recover the infinite family.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Hyperbolic 3-manifoldscharacter varietiesquaternion algebrasDehn surgeryThesis2022-09-26