On adjoint homological Selmer modules for SL${}_2$-representations of knot groups

Abstract

We introduce the adjoint homological Selmer module for an 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.

19 pages, to appear in Int. Math. Res. Not. IMRN