Extending Azumaya algebras associated to arithmetic 2-bridge links
Authors
Jiayu Wan
Abstract
Let Γ be a finitely generated group and consider the set of all characters of representations
of Γ into SL2(C). This set, denoted by X(Γ), admits an algebraic structure and is called the character
variety of Γ. When Γ is the fundamental group of a hyperbolic 3-manifold M, X(Γ) turns out to
be a powerful tool in the study of the geometry and topology of M. Chinburg-Reid-Stover have
borrowed tools from algebraic and arithmetic geometry to understand algebraic and number-theoretic
properties of the canonical curves of X(Γ). In this paper, we will partly generalize their results to
certain hyperbolic link complements, and prove that the associated canonical quaternion algebra will
not extend to an Azumaya algebra over the canonical surfaces.
