Ted Chinburg University of Pennsylvania This is a report on work with M. Stover and A. Reid on Azumaya algebras AΓ associated to knot groups Γ. Thurston defined a canonical affine curve C inside the SL2 character variety of Γ. The Azumaya algebra AΓ is defined over an open dense subset of C. I will describe some sufficient conditions for AΓ to have a continuation over a projective closure C¯¯¯¯ of C. This is possible if and only if the quaternion algebras which arise from specialization (e.g. from Dehn surgeries) are unramified outside a fixed finite set of primes. I will also discuss Brauer-Manin obstructions and elements of Tate-Shafarevitch groups arising from AΓ.