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1 - Introduction to algebraic stacks

Published online by Cambridge University Press:  05 April 2014

K. Behrend
Affiliation:
University of British Columbia
Leticia Brambila-Paz
Affiliation:
Centro de Investigación en Matemáticas A.C. (CIMAT), Mexico
Peter Newstead
Affiliation:
University of Liverpool
Richard P. Thomas
Affiliation:
Imperial College of Science, Technology and Medicine, London
Oscar García-Prada
Affiliation:
Consejo Superior de Investigaciones Cientificas, Madrid
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Moduli Spaces , pp. 1 - 131
Publisher: Cambridge University Press
Print publication year: 2014

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References

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[4] Kai, Behrend and Behrang, Noohi. Uniformization of Deligne-Mumford curves. J. Reine Angew. Math., 599:111–153, 2006.Google Scholar
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[7] J. H., Conway. The orbifold notation for surface groups. In Groups, Combinatorics and geometry (Durham, 1990), M., Liebeck and J., Saxl, eds. London Mathematical Society Lecture Notes Series vol. 165. Cambridge University Press, Cambridge, 1992, pp. 438–447.
[8] P., Deligne. Courbes elliptiques: formulaire d'après J. Tate. In Modular Functions of One Variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), B. J., Birch and W., Kuyk, eds. Lecture Notes in Mathematics, vol. 476. Springer, Berlin, 1975, pp. 53–73.
[9] P., Deligne and D., Mumford. The irreducibility of the space of curves of given genus. Inst. Hautes Études Sci. Publ. Math., 36:75–109, 1969.Google Scholar
[10] Barbara, Fantechi, Lothar, Göttsche, Luc, Illusie, Steven L., Kleiman, Nitin, Nitsure, and Angelo, Vistoli. Fundamental Algebraic Geometry. Mathematical Surveys and Monographs, vol. 123. American Mathematical Society, Providence, RI, 2005. [Grothendieck's FGA explained.]
[11] Jean, Giraud. Cohomologie non Abélienne. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, vol. 179. Springer, Berlin, 1971.
[12] Alexander, Grothendieck. Technique de descente et théorèmes d'existence en géometrie algébrique. I. Généralités. Descente par morphismes fidèlement plats. In Séminaire N. Bourbaki, Vol. 5, Exp. no. 190. Soc. Math. France, Paris, 1995, pp. 299–327.
[13] Alexander, Grothendieck. Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert. In Séminaire N. Bourbaki, Vol. 6, Exp. no. 221. Soc. Math. France, Paris, 1995, pp. 249–270.
[14] Richard, Hain. Lectures on moduli spaces of elliptic curves. In Transformation Groups and Moduli Spaces of Curves. Adv. Lect. Math. (ALM), vol. 16. International Press, Somerville, MA, 2011, pp. 95–166.
[15] R., Hartshorne. Algebraic Geometry. Graduate Texts in Mathematics no. 52. Springer-Verlag, New York, 1977.
[16] Gérard, Laumon and Laurent, Moret-Bailly. Champs Algébriques. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 39. Springer-Verlag, Berlin, 2000.
[17] Kirill C. H., Mackenzie. General Theory of Lie Groupoids and Lie Algebroids. London Mathematical Society Lecture Note Series, vol. 213. Cambridge University Press, Cambridge, 2005.
[18] I., Moerdijk and J., Mrčun. Introduction to Foliations and Lie Groupoids. Cambridge Studies in Advanced Mathematics, vol. 91. Cambridge University Press, Cambridge, 2003.
[19] D., Mumford, J., Fogarty, and F., Kirwan. Geometric Invariant Theory 3rd edn. Ergebnisse der Mathematik und ihrer Grenzgebiete (2), vol. 34. Springer-Verlag, Berlin, 1994.
[20] David, Mumford, with a section by G. M., Bergman. Lectures on Curves on an Algebraic Surface. Annals of Mathematics Studies, no. 59. Princeton University Press, Princeton, NJ, 1966.
[21] B., Noohi. Foundations of topological stacks I. arXiv:math/0503247 [math.AG].

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