Resumen de Coordinate ring of $\mathrm{SL}_2$-character varieties.

Vicente Muñoz, Jesús Martín Ovejero

• We determine generators of the coordinate ring of SL2-character varieties. In the case of the free group F3 we obtain an explicit equation of the SL2-character variety. For free groups Fk, we find transcendental generators. Finally, for the case of the 2-torus, we get an explicit equation of the SL2-character variety and use the description to compute their E-polynomials.