There are enough Azumaya algebras on surfaces

Mathematische Annalen

Volumn 321, Issue 2, 2001, Pages 439-454

  Schröer, Stefan ^a,b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035632980     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080100236     Document Type: Article

References (29)

1. M. Artin: Algebraic approximation of structures over complete local rings. Publ. Math., Inst. Hautes Étud. Sci. 36, 23-58 (1969).
2. E. Arbarello, M. Cornalba, M. Griffiths, J. Harris: Geometry of algebraic curves. Volume I. Grundlehren Math. Wiss. 267. Springer, New York, 1985.
3. E. Arbarello, M. Cornalba, M. Griffiths, J. Harris: Geometry of algebraic curves. Volume I. Grundlehren Math. Wiss. 267. Springer, New York, 1985.
4. S. Bosch, W. Lütkebohmert, M. Raynaud: Néron models. Ergeb. Math. Grenzgebiete (3) 21. Springer, Berlin, 1990.
5. F. Demeyer, T. Ford: On the Brauer group of toric varieties. Trans. Am. Math. Soc. 335, 559-577 (1993).
6. D. Edidin, B. Hasset, A. Kresh, A. Vistoli: Brauer groups and quotient stacks. Preprint math.AG/9905049.
7. O. Gabber: Some theorems on Azumaya algebras. In: M. Kervaire, M. Ojanguren (eds.), Groupe de Brauer, pp. 129-209. Lect. Notes Math. 844. Springer, Berlin, 1981.
8. J. Giraud: Cohomologie non abélienne. Grundlehren Math. Wiss. 179, Springer, Berlin, 1971.
9. A. Grothendieck, J.A. Dieudonné: Éléments de géométrie algébrique I: Le language de schémas. Grundlehren Math. Wiss. 166. Springer, Berlin, 1970.
10. A. Grothendieck: Éléments de géométrie algébrique II: Étude globale élémentaire de quelques classes de morphismes. Publ. Math., Inst. Hautes Étud. Sci. 8 (1961).
11. A. Grothendieck: Éléments de géométrie algébrique III: Étude cohomologique des faiscaux cohérent. Publ. Math., Inst. Hautes Étud. Sci. 11 (1961).
12. A. Grothendieck: Éléments de géométrie algébrique IV: Étude locale des schémas et de morphismes de schémas. Publ. Math., Inst. Hautes Étud. Sci. 32 (1967).
13. A. Grothendieck: Le groupe de Brauer I-III. In: J. Giraud (ed.) et al., Dix exposes sur la cohomologie des schemas, pp. 46-189. North-Holland, Amsterdam, 1968.
14. R. Hartshorne: Local cohomology. Lect. Notes Math. 41. Springer, Berlin, 1967.
15. R. Hartshorne: Ample subvarieties of algebraic varieties. Lect. Notes Math. 156. Springer, Berlin, 1970.
16. R. Hartshorne: Generalised divisors on Gorenstein schemes. K-Theory 8, 287-339 (1994).
17. R. Hoobler: Brauer groups of abelian schemes. Ann. Sci. Ec. Norm. Sup. 5, 45-70 (1972).
18. R. Hoobler: When is Br(X) = Br′(X)? In: F. Oystaeyen, A. Verschoren (eds.), Brauer groups in ring theory and algebraic geometry, pp. 231-244. Lect. Notes Math. 917. Springer, Berlin, 1982.
19. S. Kleiman: The transversality of a general translate. Compositio Math. 28, 287-297 (1974).
20. M.-A. Knus: Quadratic and hermitian forms over rings. Grundlehren Math. Wiss. 294. Springer, Berlin, 1991.
21. J. Lipman: Desingularization of two-dimensional schemes. Ann. Math. (2) 107, 151-207 (1978).
22. D. Mumford, J. Fogarty, F. Kirwan: Geometric invariant theory. Third edition. Ergeb. Math. Grenzgebiete (3) 34. Springer, Berlin, 1993.
23. M. Maruyama: Elementary transformations in the theory of algebraic vector bundles. In: J. Aroca, R. Buchweitz, M. Giuisti (eds.), Algebraic geometry, pp. 241-266. Lect. Notes Math. 961. Springer, Berlin, 1982.
24. J. Milne: Étale cohomology. Princeton Mathematical Series 33. Princeton University Press, Princeton, 1980.
25. M. Nagata: Imbedding of an abstract variety in a complete variety. J. Math. Kyoto Univ. 2, 1-10 (1962).
26. S. Schröer: On non-projective normal surfaces. Manuscr. Math. 100, 317-321 (1999).
27. S. Schröer: On contractible curves on normal surfaces. J. Reine Angew. Math. 524, 1-15 (2000).
28. R. Treger: Reflexive Modules. J. Alg. 54, 444-466 (1978)
29. J. Winkelmann: Every compact complex manifold admits a holomorphic vector bundle. Rev. Roum. Math. Pures Appl. 38, 743-744 (1993).