Composantes irr\'eductibles de lieux sp\'eciaux d'espaces de modules de courbes, action galoisienne en genre quelconque

TL;DR

This paper characterizes the Galois group action on specific fundamental groups of moduli spaces of marked curves, providing detailed insights into the structure of these actions in various genera.

Contribution

It offers a detailed description of the Galois action on geometric finite cyclic groups and prime order elements in genus 2, advancing understanding of fundamental group symmetries.

Findings

Galois action on geometric finite cyclic groups characterized

Action on prime order elements in genus 2 described

Insights into the structure of moduli space fundamental groups

Abstract

In this paper we characterise the action of the absolute Galois group on the geometric finite cyclic groups without \'etale 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.