On Adjoint Homological Selmer Modules for SL2-Representations of Knot Groups

We introduce the adjoint homological Selmer module for an $\textrm {SL}_2$-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module for a Galois representation. We then show finitely generated torsion-ness of our adjoint Selmer module, which are widely known as conjectures in number theory, and give some concrete examples.