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Article Dans Une Revue Contemporary mathematics Année : 2020

Examples of character varieties in characteristic $p$ and ramification

Résumé

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.

Dates et versions

hal-02133828 , version 1 (20-05-2019)

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Luisa Paoluzzi, Joan Porti. Examples of character varieties in characteristic $p$ and ramification. Contemporary mathematics, 2020, 760, pp.229-261. ⟨10.1090/conm/760⟩. ⟨hal-02133828⟩
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