On Adjoint Homological Selmer Modules for <b>SL</b>2-Representations of Knot Groups-Reference-Cited by-同舟云学术

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

Published:2022-09-22 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Kitayama Takahiro¹,Morishita Masanori²,Tange Ryoto¹³,Terashima Yuji⁴

Affiliation:

1. Graduate School of Mathematical Sciences , the University of Tokyo, 3-8-1, Komaba, Meguro-ku, Tokyo 153-8914, Japan

2. Faculty of Mathematics , Kyushu University, 744, Motooka, Nishi-ku, Fukuoka 819-0395, Japan

3. Department of Mathematics , School of Education, Waseda University, 1-104, Totsuka-cho, Shinjuku-ku, Tokyo 169-8050, Japan

4. Graduate School of Science , Tohoku University, 6-3, Aoba, Aramaki-aza, Aoba-ku, Sendai 980-8578, Japan

Abstract

Abstract 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.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac255/45972696/rnac255.pdf

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