Profinite complexes of curves, their automorphisms and anabelian properties of moduli stacks of curves

M. Boggi, P. Lochak

Let ${\mathcal{M}}_{g,[n]}$, for $2g-2+n>0$, be the D-M moduli stack of smooth curves of genus $g$ labeled by $n$ unordered distinct points. The main result of the paper is that a finit…