This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector bundles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.
This is a preview of subscription content, log in via an institution to check access.
Access this article Subscribe and saveSpringer+
from €39.99 /Month
Price includes VAT (Germany)
Instant access to the full article PDF.
Similar content being viewed by others ReferencesArtin M, Algebraic Spaces, Yale Math. Monographs 3 (Yale University Press), (1971)
Artin M, Versal deformations and algebraic stacks,Invent. Math.27 (1974) 165–189
Deligne P and Mumford D, The irreducibility of the space of curves of given genus,Publ. Math. IHES 36 (1969) 75–110
Edidin D, Notes on the construction of the moduli space of curves, preprint (1999)
Giraud J, Cohomologie non abélienne, Die Grundlehren der Mathematischen Wissenschaften, Band 179 (Springer Verlag) (1971)
Hakim M, Topos annelés et schémas relatifs, Ergebnisse der Math. und ihrer Grenzgebiete 64 (Springer Verlag) (1972)
Hartshorne R, Algebraic geometry, Grad. Texts in Math. 52 (Springer Verlag) (1977)
Huybrechts D and Lehn M, The geometry of moduli spaces of sheaves, Aspects of Mathematics E31 (Vieweg, Braunschweig/Wiesbaden) (1997)
Knutson D, Algebraic spaces, LNM 203 (Springer Verlag) (1971)
Laumon G, Champs algébriques, Prépublications 88-33, (U. Paris-Sud) (1988)
Laumon G and Moret-Bailly L, Champs algébriques, Ergegnisse der Math. und ihrer Grenzgebiete. 3. Folge, 39 (Springer Verlag) (2000)
Mac Lane S and Moerdijk I, Sheaves in Geometry and Logic, Universitext, Springer-Verlag, 1992
Simpson C, Moduli of representations of the fundamental group of a smooth projective variety I,Publ. Math. I.H.E.S. 79 (1994) 47–129
Tamme G, Introduction to Etale Cohomology, Universitext (Springer-Verlag) (1994)
Vistoli A, Intersection theory on algebraic stacks and their moduli spaces,Invent. Math. 97 (1989) 613–670
Tata Institute of Fundamental Research, Homi Bhabha Road, 400 005, Mumbai, India
Tomás L Gómez
Correspondence to Tomás L Gómez.
About this article Cite this articleGómez, T.L. Algebraic stacks. Proc Math Sci 111, 1–31 (2001). https://doi.org/10.1007/BF02829538
Received: 16 February 2000
Revised: 24 August 2000
Issue Date: February 2001
DOI: https://doi.org/10.1007/BF02829538
RetroSearch is an open source project built by @garambo | Open a GitHub Issue
Search and Browse the WWW like it's 1997 | Search results from DuckDuckGo
HTML:
3.2
| Encoding:
UTF-8
| Version:
0.7.4