Skip to main content

Some New Hasse Principles For Conic Bundle Surfaces

  • Chapter

Part of the book series: Progress in Mathematics ((PM,volume 81))

Abstract

Let k be a number field and let X be a smooth projective geometrically integral variety defined over k. If K is an overfield of k, denote by X(K) the set of K—points on X.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. J-L. Colliot-Thélène — Quelques propriétés arithmttiques des surfaces rationnelles (d’aprés Manin), Séminaire de Théorie des Nombres, Bordeaux 1972–72, Exp. 13, Lab. Theorie des Nombres, C.N.R.S., Talence 1972.

    Google Scholar 

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

    Google Scholar 

  3. J.-L. Colliot-Thélène, D. Coray, J.-J. Sansuc.- Descente et principe de Hasse pour certaines variétés rationnelles, J. reine angew. Math., 320 (1980), 150–191.

    Google Scholar 

  4. J.-L. Colliot-Thelene, D. Kanevsky, J.-J. Sansuc.— Arithmétique des surfaces cubiques diagonales, in Diophantine Approximation and Transcendence Theory, G. Wüstholz ed., Springer Lecture Notes in Mathematics 1290 (1987), 1–108.

    Google Scholar 

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

    Google Scholar 

  6. J.-L. Colliot-Thélène, J.-J. Sansuc — La descente sur les surfaces rationnelles fibr&es en coniques, C.R. Acad. Sci. Paris 303, Serie I 1986, 303–306.

    Google Scholar 

  7. J.-L. Colliot-Thélène, J.-J. Sansuc.— La descente sur les varieties rationnelles, II, Duke Math. J. 54 (1987), 375–492.

    Google Scholar 

  8. J.-L. Colliot-Thelene, J-J. Sansuc, Sir Peter Swinnerton-Dyer - Intersections of two quadrics and Ch&telet surfaces, J. reine angew. Math. 373 (1987), 37–107 et 374 (1987), 72–168.

    Google Scholar 

  9. 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 

  10. S. Lang - Algebraic number theory, Addison-Wesley, Reading 1970.

    Google Scholar 

  11. Yu.I. Manin — Rational surfaces over perfect fields (Russian), Inst.des Hautes Etudes Sci., Publ. Math. 30 (1966), 55–113 (engl. transl.: Translations AMS (2) 84 (1969) 137–186

    Google Scholar 

  12. Yu.I. Manin.— Le groupe de Brauer-Grothendieck en géomttrie diophantienne, in Actes du congrès intern, math, Nice 1,

    Google Scholar 

  13. Yu.I. Manin, M.A. Tsfasman— Rational varieties: Algebra, geometry and arithmetic, Uspekhi Mat. Nauk 41 (1986), 43–94 (engl. transl.: Russian Math. Surveys 41 (1986), 51–116).

    Google Scholar 

  14. S. Saito.— Some observations on motivic cohomologies of arithmetical schemes, preprint.

    Google Scholar 

  15. P. Salberger— K-theory of orders and their Brauer-Severi schemes, Thesis, Department of Mathematics, University of Goteborg 1985.

    Google Scholar 

  16. P. Salberger — Sur l’arithmétique de certaines surfaces de del Pezzo, C.R. Acad. Sci. Paris 303, série I (1986), 273–276.

    Google Scholar 

  17. P. Salberger.— On the arithmetic of conic bundle surfaces, in Séminaire de Théorie des Nombres Paris 1985–86, Progr. Math. 71, Birkhaüser, Basel Boston 1987, 175–197 (cf. also the Errata in this volume).

    Google Scholar 

  18. P. Salberger — Zero-cycles on rational surfaces over number fields, Invent. Math. 91 (1988), 505–524.

    Article  MathSciNet  MATH  Google Scholar 

  19. J J.-J. Sansuc.— Descente et principe de Hasse pour certaines varieties rationnelles, in Séminaire de Théorie des Nombres, Paris 1980–81, Progr. Math. 22, Birkhäuser, Basel Boston 1982, 253–271.

    Google Scholar 

  20. J.-J. Sansuc.— A propos d’une conjecture arithmttique sur le groupe de Chow d’une surface rationnelle, Séminaire de Théorie des Nombres, Bordeaux 1981–81, Exp. 33 Lab. Theorie des Nombres, C.N.R.S., Talence 1972.

    Google Scholar 

  21. W.M. Schmidt. — The density of integer points on homogeneous varieties, Acta Math. 154 (1985), 243–296.

    Article  MathSciNet  MATH  Google Scholar 

  22. J-P. Serre.— Corps locaux, deuxiéme éd, Herman, Paris 1968

    Google Scholar 

  23. J. Silverman - The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106, Springer-Verlag, Berlin Heidelberg New York 1986.

    Google Scholar 

  24. T.A. Springer.— Sur les formes quadratiques d’indice zero, C.R. Acad. Sci. 234, 1517–1519 (1952).

    Google Scholar 

  25. H.P.F. Swinnerton—Dyer — Rational points on del Pezzo surfaces of degree 5, in Algebraic geometry Oslo,

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Birkhäuser Boston

About this chapter

Cite this chapter

Salberger, P. (1990). Some New Hasse Principles For Conic Bundle Surfaces. In: Goldstein, C. (eds) Séminaire de Théorie des Nombres, Paris 1987–88. Progress in Mathematics, vol 81. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3460-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3460-9_14

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8032-3

  • Online ISBN: 978-1-4612-3460-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics