Composantes irréductibles de lieux spéciaux d’espaces de modules de courbes, action galoisienne en genre quelconque

Collas, Benjamin ; Maugeais, Sylvain

Annales de l'Institut Fourier, Tome 65 (2015), p. 245-276 / Harvested from Numdam

Résumé

Dans cet article, nous caractérisons l’action du groupe de Galois absolu sur les groupes d’inertie champêtre géométriques cycliques et sans factorisation étale du groupe fondamental géométrique des espaces de modules de courbes marquées. Nous établissons par ailleurs la même action sur les éléments de torsion profinis d’ordre premier en genre $2$.

Abstract

In this paper we characterise the action of the absolute Galois group on the geometric finite cyclic groups without étale factorization of stack inertia of the profinite geometric fundamental group of moduli spaces of marked curves. As a complementary result, we give the same action on prime order profinite elements in genus 2.

Détail

Publié le : 2015-01-01

Zbl 1326.11069

DOI : https://doi.org/10.5802/aif.2930
Classification:  11R32,  14H10,  14H30,  14H45
Mots clés: groupe fondamental algébrique, inertie champêtre, lieu spécial, groupes bons

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