Examples of character varieties in characteristic $p$ and ramification

Abstract

We study SL2(F)-character varieties of knots over algebraically closed fields F. We give a sufficient condition in terms of the double branched cover of a 2-bridge knot (or, equivalently, of its Alexander polynomial) on the characteristic of F, an odd prime, for the SL2(F)-character variety to present ramification phenomena. Finally we provide several explicit computations of character varieties to illustrate the result, exhibiting also other types of ramification.