On Galois action on stack inertia of moduli spaces of curves
Abstract
We establish that the geometric action of the absolute Galois group on the étale fundamental group of moduli spaces of curves induces a Galois action on its stack inertia subgroups, and that this action is given by cyclotomy conjugacy. This result extends the special case of inertia without étale factorisation previously established by the authors. It is here obtained in the general case by comparing deformations of Galois actions. Since the stack inertia corresponds to the first level of the stack stratification of the space, this results, by analogy with the arithmetic of the DeligneMumford stratification, opens the way to a systematic Galois study of the stack inertia through the corresponding stratification of the moduli stack
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.4644
 Bibcode:
 2014arXiv1412.4644C
 Keywords:

 Mathematics  Algebraic Geometry;
 11R32;
 14H10;
 14H30;
 14H45
 EPrint:
 23 pages, 3 figures