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

Takahiro Kitayama; Masanori Morishita; Ryoto Tange; Yuji Terashima

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arXiv · 2205.05401

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

Takahiro Kitayama·Masanori Morishita·Ryoto Tange·Yuji Terashima

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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.

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Takahiro Kitayama, Masanori Morishita, Ryoto Tange, Yuji Terashima. 2022-05-11. On adjoint homological Selmer modules for SL$_2$-representations of knot groups. https://arxiv.org/abs/2205.05401

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