Abstract
For an algebraic stack \({\fancyscript{X}}\) flat and of finite presentation over a scheme S, we introduce various notions of relative connected components and 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 \({\fancyscript{X}}\). 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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