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We consider the adjoint homological Selmer module for an \(\textrm{SL}_2\) -augmented tautological 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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On Adjoint Homological Selmer Modules for  \(\textrm{SL}_2\) -Augmented Tautological Representations of Knot Groups

  • 会议论文

  • 发表日期：

    2025年

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  • Ryoto Tange

摘要

We consider the adjoint homological Selmer module for an \(\textrm{SL}_2\) -augmented tautological 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.