Skip to main content
SpringerLink
Log in
Book cover

Séminaire de Théorie des Nombres, Paris 1985–86 pp 175–197Cite as

Birkhäuser

On the Arithmetic of Conic Bundle Surfaces

  • Chapter

Part of the book series: Progress in Mathematics ((PM,volume 71))

Abstract

Let k be a perfect field and \(\bar k\)an algebraic closure of k.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. S. Bloch.- On the Chow groups of certain rational surfaces, Ann. Sc. Bc. Norm. Sup. (4) 14 (1981), 41–59.

    Google Scholar 

  2. J. Brzezinski.- Arithmetical quadratic surfaces of genus 0, I, Math. Scand. 46 (1980), 183–208.

    Google Scholar 

  3. [Bt]H. Bass, J. Tate.- The Milnor ring of a global field, in Lecture Notes in Mathematics 342, Springer-Verlag, Berlin-Heidelberg-New York 1973.

    Google Scholar 

  4. J.-L. Colliot-Thélène, D. Coray.- L’équivalence rationnelle sur les points fermés des surfaces rationnelles fibrées en coniques, Compositio Math. 39 (1979), 301–332.

    MathSciNet  MATH  Google Scholar 

  5. J.-L. Colliot-Thélène, D. Kanevsky, J.-J. Sansuc.Arithmétique des surfaces cubiques diagonales, to appear in Lecture Notes in Mathematics (ed. G. WUstholz), Springer-Verlag.

    Google Scholar 

  6. [Co]J.-L. Colliot-Thélène.- Hilbert’s theorem 90 for K2, with application to the Chow groups of rational surfaces, Invent. Math. 71 (1983), 1–20.

    Google Scholar 

  7. J.-L. Colliot-Thélène, J.-J. Sansuc.- On the Chow groups of certain rational surfaces: a sequel to a paper of S. Bloch, Duke Math. J. 48 (1981), 421–447.

    MATH  Google Scholar 

  8. [CSS]J.-L. Colliot-Thélène, J.-J. Sansuc, Sir Peter Swinnerton-Dyer.- Intersections of two quadrics and ChMtelet surfaces, J. reine angew. Math. 373 (1987), 37–107 and 374 (1987), 72–168 (cf. C.R. Acad. Sci. Paris: Série I, Math. 298 (1984), 377–380 ).

    MATH  Google Scholar 

  9. V.A. Iskovskih.- Rational surfaces with a pencil of rational curves, Mat. Sbornik 74 (1967), 608–638 (eng. transl: Math. USSR-Sbornik 3 (1967), 563–587 ).

    Google Scholar 

  10. V.A. Iskovskih.- Minimal models of rational surfaces over arbitrary fields, Izv. Ak. Nauk. SSSR Ser. Mat. 43 (1979), 19–43 (engl. transl: Math.-USSR Izv. 14 (1980), 17–39 ).

    Google Scholar 

  11. [Ka]K. Kato.- A generalization of local class field theory by using K-groups II, J. Fac. Sci. Univ. Tokyo, Sec. IA 27 Nc 3 (1980), 603–683.

    Google Scholar 

  12. [KST]B.E. Kunyayskii, A.N. Skorobogatov, M.A. Tsfasman.Combinatorics and geometry of Del Pezzo surfaces of degree 4, Uspekhi Mat. Nauk 40: 6 (1985), 145–46 (engl. transl.: in Russian Math. Surveys 40: 6 (1985), 131–132 ).

    Article  Google Scholar 

  13. Yu.I. Manin.- Le groupe de Brauer-Grothendieck en géométrie diophantienne, in Actes du Congrès Intern. Math. (Nice, 1970 ), Gauthiers-Villars, Paris, 1971, tome 1, 401–411.

    Google Scholar 

  14. Yu.I. Manin.- Cubic forms: algebra, geometry, arithmetic, second ed., North-Holland, Amsterdam-London, 1986.

    Google Scholar 

  15. H. Mattson.- A generalization of the Riemann-Roch theorem Ill. J. Math. 5 (1961), 355–375.

    MathSciNet  MATH  Google Scholar 

  16. J. Milnor.- Algebraic K-theory and quadratic forms, Invent. Math. 9 (1970), 318–344.

    Article  MathSciNet  Google Scholar 

  17. Yu.I. Manin, M.A. Tsfasman.- Rational varieties: algebra, geometry, arithmetic, Uspekhi Mat. Nauk. 41 (1986) 43–94 (engl. transi in Russian Math. Surveys 41: 2 (1986), 51–116 ).

    Article  MathSciNet  MATH  Google Scholar 

  18. D. Quillen.- Higher algebraic K-theory I, in Lecture Notes in Mathematics 341, Springer-Verlag, Berlin-Heidelberg-New York 1973.

    Google Scholar 

  19. I. Reiner.- Maximal orders, Academic Press, London 1975.

    Google Scholar 

  20. P. Salberger.- K-theory of orders and their Brauer-Severi schemes, Thesis, Dept. of Math., Univ. of Göteborg, 1985.

    Google Scholar 

  21. P. Salberger.- Galois descent and class groups of orders, in Lecture Notes in Math. 1142, Springer-Verlag, Berlin-Heidelberg-New York 1985.

    Google Scholar 

  22. P. Salberger.- Sur l’arithmétique de certaines surfaces de del Pezzo, C.R. Acad. Sci. Paris, Série I, Math. 303 (1986), 273–276.

    Google Scholar 

  23. C. Sherman.- Some theorems on the K-theory of coherent sheaves, Comm. in Alg. 7 (1979), 1489–1508.

    Article  MathSciNet  MATH  Google Scholar 

  24. J. Tate.- The cohomology groups of tori in finite Galois extension of number fields, Nagoya Math. J. 27 (1966), 709–719.

    MathSciNet  MATH  Google Scholar 

  25. M. Van den Bergh, J. Van Geel.- Division algebras over function fields, Isr. J. Math. 52 (1985), 33–45.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Université de Paris-Sud, 91405, Orsay Cedex, France

    Per Salberger

Authors
  1. Per Salberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Centre d’Orsay, Université de Paris-Sud, F-91405, Orsay Cedex, France

    Catherine Goldstein

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer Science+Business Media New York

About this chapter

Cite this chapter

Salberger, P. (1987). On the Arithmetic of Conic Bundle Surfaces. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1985–86. Progress in Mathematics, vol 71. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-4267-1_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4267-1_13

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4757-4268-8

  • Online ISBN: 978-1-4757-4267-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation