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Manuscripta Mathematica

, Volume 136, Issue 1–2, pp 1–32 | Cite as

Composantes connexes et irréductibles en familles

  • Matthieu RomagnyEmail author
Article

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.

Mathematics Subject Classification

14A20 14D06 14H10 14D22 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Institut de Mathématiques de Jussieu, Théorie des NombresUniversité Pierre et Marie CurieParis Cedex 05France

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