Paola Frediani, Frank Neumann
Etale homotopy types of moduli stacks of algebraic curves with symmetries
Preprint series: Mathematica Gottingensis
14F35 Homotopy theory; fundamental groups, See also {14E20,
14H10 Families, moduli (algebraic)
Abstract: Using the machinery of etale homotopy theory \`a la
Artin-Mazur we determine the etale homotopy types of moduli
stacks over $\overline{\Bbb{Q}}$ parametrizing families of
algebraic curves of genus $g \geq 2$ endowed with an action
of a finite group $G$ of automorphisms, which comes with a
fixed embedding in the mapping class group $\Gamma_g$, such
that in the associated complex analytic situation the action
of $G$ is precisely the differentiable action induced by
this specified embedding of $G$ in $\Gamma_g$.
Keywords: algebraic curves, etale homotopy theory, algebraic stacks, moduli of algebraic curves, Teichm\"uller theory