Etale homotopy types of moduli stacks of algebraic curves with symmetries

Details Etale homotopy types of moduli stacks of algebraic curves with symmetries Etale homotopy types of moduli stacks of algebraic curves with symmetries

2004-04-21

arxiv.org/abs/math/0404387v1

K-Theory 30: 315-340, 2003

Mathematics

Algebraic Geometry

27 pages

Scientific paper

Using the machinery of etale homotopy theory a' la Artin-Mazur we determine the etale homotopy types of moduli stacks over $\bar{\Q}$ parametrizing families of algebraic curves of genus g greater than 1 endowed with an action of a finite group G of automorphisms, which comes with a fixed embedding in the mapping class group, 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 the mapping class group.

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