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arXiv · 0912.2605

Composantes connexes et irréductibles en familles

Matthieu Romagny
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Abstract

For an algebraic stack $\sX$ flat and of finite presentation over a scheme $S$, we introduce various notions of {\em relative connected components} and {\em relative irreducible components}. The main distinction between these notions is whether we require the total space of a relative component to be open or closed in $\sX$. We study the representability of the associated functors of relative components, and give an application to the moduli stack of curves of genus $g$ admitting an action of a fixed finite group $G$.

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Matthieu Romagny. 2010-02-18. Composantes connexes et irréductibles en familles. https://arxiv.org/abs/0912.2605

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