On octahedral extensions of ℚ and quadratic ℚ-curves
Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 125-131.

On donne une condition nécessaire pour qu’une représentation surjective Gal(ℚ ¯/ℚ)→ PGL 2 (𝔽 3 ) provienne de la 3-torsion d’une ℚ-courbe. Nous étudions plus particulièrement le cas des ℚ-courbes quadratiques.

We give a necessary condition for a surjective representation Gal(ℚ ¯/ℚ)→ PGL 2 (𝔽 3 ) to arise from the 3-torsion of a ℚ-curve. We pay a special attention to the case of quadratic ℚ-curves.

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     author = {Julio Fern\'andez},
     title = {On octahedral extensions of $\mathbb {Q}$ and quadratic $\mathbb {Q}$-curves},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
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     publisher = {Universit\'e Bordeaux I},
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Julio Fernández. On octahedral extensions of $\mathbb {Q}$ and quadratic $\mathbb {Q}$-curves. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 125-131. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_1_125_0/

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