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 | |
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