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arXiv · 0708.0093

Note sur la détermination algébrique du groupe fondamental pro-résoluble d'une courbe affine

Niels Borne·Michel Emsalem
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Abstract

Let X be a smooth projective algebraic curve of genus g minus $r\geq 1$ points defined over an algebraically closed field k of characteristic $p\geq 0$. The structure of the largest prime to p quotient of the étale fundamental group is well known by transcendental methods : it is isomorphic to the largest prime to p quotient of a free pro-finite group on 2g+r-1 generators. We show that, with purely algebraic means, we can prove the corresponding result for the largest pro-solvable quotient of these groups.

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Niels Borne, Michel Emsalem. 2008-05-07. Note sur la détermination algébrique du groupe fondamental pro-résoluble d'une courbe affine. https://arxiv.org/abs/0708.0093

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