Examples of character varieties in characteristic $p$ and ramification

Luisa Paoluzzi; Joan Porti

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arXiv · 1905.07196

Examples of character varieties in characteristic $p$ and ramification

Luisa Paoluzzi·Joan Porti

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Abstract

We study $\mathrm{SL}_2(\mathbb{F})$-character varieties of knots over algebraically closed fields $\mathbb{F}$. 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 $\mathbb{F}$, an odd prime, for the $\mathrm{SL}_2(\mathbb{F})$-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.

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Luisa Paoluzzi, Joan Porti. 2019-05-17. Examples of character varieties in characteristic $p$ and ramification. https://arxiv.org/abs/1905.07196

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