On certain l-functions for deformations of knot group representations

Takahiro Kitayama; Masanori Morishita; Ryoto Tange; Yuji Terashima

doi:10.1090/tran/7037

On certain l-functions for deformations of knot group representations

Takahiro Kitayama, Masanori Morishita, Ryoto Tange, Yuji Terashima

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study the twisted knot module for the universal deformation of an SL₂ -representation of a knot group and introduce an associated L-function, which may be seen as an analogue of the algebraic p-adic L-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L-function by some concrete examples for 2-bridge knots.

Original language	English
Pages (from-to)	3171-3195
Number of pages	25
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	5
DOIs	https://doi.org/10.1090/tran/7037
Publication status	Published - 2018 May
Externally published	Yes

Keywords

Character schemes
Deformations of representations
L-functions
Twisted Alexander invariants
Twisted knot modules

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/tran/7037

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title = "On certain l-functions for deformations of knot group representations",

abstract = "We study the twisted knot module for the universal deformation of an SL2 -representation of a knot group and introduce an associated L-function, which may be seen as an analogue of the algebraic p-adic L-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L-function by some concrete examples for 2-bridge knots.",

keywords = "Character schemes, Deformations of representations, L-functions, Twisted Alexander invariants, Twisted knot modules",

author = "Takahiro Kitayama and Masanori Morishita and Ryoto Tange and Yuji Terashima",

note = "Funding Information: Received by the editors December 17, 2015, and, in revised form, February 8, 2016 and July 22, 2016. 2010 Mathematics Subject Classification. Primary 57M25. Key words and phrases. Deformations of representations, character schemes, twisted knot modules, twisted Alexander invariants, L-functions. The first author was partly supported by JSPS Research Fellowships for Young Scientists 26800032. The second author was partly supported by Grants-in-Aid for Scientific Research (B) 24340005. The fourth author was partly supported by Grants-in-Aid for Scientific Research (C) 25400083. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2018",

month = may,

doi = "10.1090/tran/7037",

language = "English",

volume = "370",

pages = "3171--3195",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "5",

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TY - JOUR

T1 - On certain l-functions for deformations of knot group representations

AU - Kitayama, Takahiro

AU - Morishita, Masanori

AU - Tange, Ryoto

AU - Terashima, Yuji

N1 - Funding Information: Received by the editors December 17, 2015, and, in revised form, February 8, 2016 and July 22, 2016. 2010 Mathematics Subject Classification. Primary 57M25. Key words and phrases. Deformations of representations, character schemes, twisted knot modules, twisted Alexander invariants, L-functions. The first author was partly supported by JSPS Research Fellowships for Young Scientists 26800032. The second author was partly supported by Grants-in-Aid for Scientific Research (B) 24340005. The fourth author was partly supported by Grants-in-Aid for Scientific Research (C) 25400083. Publisher Copyright: © 2017 American Mathematical Society.

PY - 2018/5

Y1 - 2018/5

N2 - We study the twisted knot module for the universal deformation of an SL2 -representation of a knot group and introduce an associated L-function, which may be seen as an analogue of the algebraic p-adic L-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L-function by some concrete examples for 2-bridge knots.

AB - We study the twisted knot module for the universal deformation of an SL2 -representation of a knot group and introduce an associated L-function, which may be seen as an analogue of the algebraic p-adic L-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L-function by some concrete examples for 2-bridge knots.

KW - Character schemes

KW - Deformations of representations

KW - L-functions

KW - Twisted Alexander invariants

KW - Twisted knot modules

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DO - 10.1090/tran/7037

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SP - 3171

EP - 3195

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 5

ER -

On certain l-functions for deformations of knot group representations

Abstract

Keywords

ASJC Scopus subject areas

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