Skip to main content

On the Brauer group of surfaces and subrings of k[x,y]

  • Conference paper
  • First Online:
Brauer Groups in Ring Theory and Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 917))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Artin and D. Mumford, Some elementary examples of unirational varieties which are not rational, Proc. London Math. Soc. 25 (1972), 75–95.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Auslander, The Brauer group of a ringed space, J. Algebra 4 (1966), 220–273.

    Article  MathSciNet  MATH  Google Scholar 

  3. -, Central separable algebras which are locally endomorphism rings of free modules, Proc. A.M.S. 30 (1971), 395–404.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Auslander and O. Goldman, The Brauer group of a commutative ring, Trans. A.M.S. 97 (1960), 367–409.

    Article  MathSciNet  MATH  Google Scholar 

  5. E. Brieskorn, Rational singularitäten Komplexer flächen, Inventiones Math. 4 (1968), 336–358.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. N. Childs, Mayer-Vietoris sequences and Brauer groups of non normal domains, Trans. A.M.S. 196 (1974), 51–67.

    Article  MathSciNet  MATH  Google Scholar 

  7. -, On Brauer groups of some normal local rings, Brauer groups (Evanston, 1975), Lecture Notes in Math., Vol. 549, Springer-Verlag, New York, 1976, 1–15.

    Google Scholar 

  8. V. I. Danilov, The group of ideal classes of a completed ring, Math. USSR Sbornik, 6 (1968), 493–500.

    Article  MATH  Google Scholar 

  9. -, Rings with a discrete group of ideal classes, Math. USSR Sbornik, 12 (1970), 368–386.

    Article  MATH  Google Scholar 

  10. -, On rings with a discrete divisor class group, Math. USSR Sbornik, 17 (1972), 228–236.

    Article  MATH  Google Scholar 

  11. P. Deligne et al., SGA 4 1/2, Cohomologie étale, Lecture Notes in Math., Vol. 569, Springer-Verlag.

    Google Scholar 

  12. F. R. DeMeyer and T. J. Ford, The Brauer group of a surface, Technical Report #8, Colorado State University, 1981.

    Google Scholar 

  13. T. Ford, Every finite abelian group is the Brauer group of a ring, Proc. A.M.S. 82 (1981), 315–321.

    Article  MathSciNet  MATH  Google Scholar 

  14. O. Gabber, Some theorems on Azumaya algebras, Ph.D. thesis, Harvard University, 1978.

    Google Scholar 

  15. W. Gordon, Brauer groups of local rings with conelike singularities, preprint.

    Google Scholar 

  16. P. Griffith, The Brauer group of A[T], Math. Zeitschrift, 147 (1976), 79–86.

    Article  MathSciNet  MATH  Google Scholar 

  17. A. Grothendieck, Le group de Brauer I, II, III, Dix exposés sur la Cohomologie des Schemas, North-Holland, Amsterdam; Masson, Paris, 1968, 46–188.

    Google Scholar 

  18. R. Hartshorne, Algebraic geometry, Springer-Verlag, New York, 1977.

    Book  MATH  Google Scholar 

  19. M. A. Knus and M. Ojanguren, A Mayer-Vietoris sequence for the Brauer group, J. Pure Appl. Algebra 5 (1974), 345–360.

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ. Math IHES 36 (1969), 195–279.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Milne, Étale cohomology, Princeton University Press, Princeton, 1980.

    MATH  Google Scholar 

  22. D. Mumford, The topology of normal singularities of an algebraic surface and a criterion for simplicity, Publ. Math. IHES 9 (1961), 5–22.

    Article  MathSciNet  MATH  Google Scholar 

  23. D. Prill, Local classification of quotients of complex manifolds by discontinuous groups, Duke Math. J. 34 (1967), 375–386.

    Article  MathSciNet  MATH  Google Scholar 

  24. P. Russell, On affine-ruled rational surfaces, preprint.

    Google Scholar 

  25. R. Treger, Reflexive modules, J. Algebra 54 (1978), 444–466.

    Article  MathSciNet  MATH  Google Scholar 

  26. -, On p-torsion in étale cohomology and in the Brauer group, Prox. A.M.S. 78 (1980), 189–192.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Freddy M. J. van Oystaeyen Alain H. M. J. Verschoren

Additional information

Dedicated to Goro Azumaya

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

DeMeyer, F.R., Ford, T.J. (1982). On the Brauer group of surfaces and subrings of k[x,y]. In: van Oystaeyen, F.M.J., Verschoren, A.H.M.J. (eds) Brauer Groups in Ring Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 917. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092236

Download citation

  • DOI: https://doi.org/10.1007/BFb0092236

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11216-7

  • Online ISBN: 978-3-540-39057-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics