Composantes connexes et irréductibles en familles

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• 作者：1. Institut de Mathématiques de Jussieu ; Théorie des Nombres ; Université Pierre et Marie Curie ; Case 82 ; 4 ; Place Jussieu ; 75252 Paris Cedex 05 ; France
• 关键词：14A20 – 14D06 – 14H10 – 14D22
• 刊名：manuscripta mathematica
• 出版年：2011
• 出版时间：September 2011
• 年：2011
• 卷：136
• 期：1-2
• 页码：1-32
• 全文大小：362.0 KB
• 参考文献：1. Abramovich D., Olsson M., Vistoli A.: Tame stacks in positive characteristic. Ann. Inst. Fourier (Grenoble) 58(4), 1057–1091 (2008)
  2. Artin M.: Versal deformations and algebraic stacks. Invent. Math. 27, 165–189 (1974)
  3. Bertin, J., Romagny, M.: Champs de Hurwitz, prépublication disponible à l’adresse http://people.math.jussieu.fr/~romagny/
  4. Brochard S.: Foncteur de Picard d’un champ algébrique. Math. Ann. 343, 541–602 (2009)
  5. Deligne P., Mumford D.: The irreducibility of the space of curves of given genus. Publ. Math. IHéS 36, 75–109 (1969)
  6. Dieudonné, J., Grothendieck, A.: éléments de Géométrie Algébrique II, III, IV, Publ. Math. IHéS 8 (1961), 17 (1963), 24 (1965), 28 (1966), 32 (1967)
  7. Eisenbud D.: Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in mathematics. Springer, Berlin (1995)
  8. Keel S., Mori S.: Quotients by groupoids. Ann. Math. (2) 145(1), 193–213 (1997)
  9. Knutson, D.: Algebraic Spaces. Lecture Notes in Mathematics, vol. 203. Springer, Berlin (1971)
  10. Laszlo Y.: Linearization of group stack actions and the Picard group of the moduli of SL r /μ s -bundles on a curve. Bull. Soc. Math. Fr. 125(4), 529–545 (1997)
  11. Laumon, G., Moret-Bailly, L.: Champs algébriques, Ergebnisse der Mathematik und ihrer Grenzgebiete (3. Folge) no. 39. Springer, Berlin (2000)
  12. Lieblich M.: Moduli of twisted sheaves. Duke Math. J. 138(1), 23–118 (2007)
  13. Magaard, K., Shaska, T., Shpectorov, S., V?lklein, H.: The locus of curves with prescribed automorphism group, Communications in arithmetic fundamental groups (Kyoto, 1999/2001). Sūrikaisekikenkyūsho Kōkyūroku no. 1267, pp. 112–141 (2002)
  14. Olsson M.: On proper coverings of Artin stacks. Adv. Math. 198(1), 93–106 (2005)
  15. Raynaud M., Gruson L.: Critères de platitude et de projectivité. Techniques de ?platification? d’un module. Invent. Math. 13, 1–89 (1971)
  16. Romagny M.: Group actions on stacks and applications. Mich. Math. J. 53(1), 209–236 (2005)
  17. Romagny, M.: Effective models of group schemes. to appear in J. Algebraic Geom.
  18. To?n, B., Vezzosi, G.: Homotopical algebraic geometry II. Geometric stacks and applications. Mem. Am. Math. Soc. 193(902), x+224 pp (2008)
• 作者单位：http://www.springerlink.com/content/y3702277731t6225/
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebraic Geometry
  Topological Groups and Lie Groups
  Geometry
  Number Theory
  Calculus of Variations and Optimal Control
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-1785

文摘

For an algebraic stack \fancyscriptX{\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 \fancyscriptX{\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.