Principe de Hasse et approximation faible sur certaines hypersurfaces

David Harari

Annales de la Faculté des sciences de Toulouse : Mathématiques (1995)

  • Volume: 4, Issue: 4, page 731-762
  • ISSN: 0240-2963

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Harari, David. "Principe de Hasse et approximation faible sur certaines hypersurfaces." Annales de la Faculté des sciences de Toulouse : Mathématiques 4.4 (1995): 731-762. <http://eudml.org/doc/73365>.

@article{Harari1995,
author = {Harari, David},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Hasse principle; weak approximation; Brauer group; affine hypersurfaces; Brauer-Manin obstruction},
language = {fre},
number = {4},
pages = {731-762},
publisher = {UNIVERSITE PAUL SABATIER},
title = {Principe de Hasse et approximation faible sur certaines hypersurfaces},
url = {http://eudml.org/doc/73365},
volume = {4},
year = {1995},
}

TY - JOUR
AU - Harari, David
TI - Principe de Hasse et approximation faible sur certaines hypersurfaces
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1995
PB - UNIVERSITE PAUL SABATIER
VL - 4
IS - 4
SP - 731
EP - 762
LA - fre
KW - Hasse principle; weak approximation; Brauer group; affine hypersurfaces; Brauer-Manin obstruction
UR - http://eudml.org/doc/73365
ER -

References

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  1. [1] Amer ( M.) .— Quadratische Formen über Funktionenkörpern, Dissertation, Mainz (1976). 
  2. [2] Brumer ( A.) .— Remarques sur les couples de formes quadratiques, C.R. Acad. Sci.Paris286, série A (1978), pp. 679-681. Zbl0392.10021MR498374
  3. [3] Cassels J ( W.S.) et Fröhlich ( A.) .- Algebraic number theory, Academic Press, London and New York (1967). Zbl0153.07403MR215665
  4. [4] Colliot-Thélène ( J.-L.) .— Surfaces rationnelles fibrées en coniques, Séminaire de théorie des nombres de Paris 1988-1989, éd. C. Goldstein, Progress in Math, Birkhäuser91 (1990), pp. 43-55. Zbl0731.14033MR1104699
  5. [5] Colliot-Thélène ( J.-L.), Coray ( D.) et Sansuc ( J.-J.) .— Descente et principe de Hasse pour certaines variétés rationnelles, J. Reine Angew. Math.320 (1980), pp. 150-191. Zbl0434.14019MR592151
  6. [6] Colliot-Thélène ( J.-L.) et Salberger ( P.) .— Arithmetic on singular cubic hypersurfaces, Proc. London Math. Soc.58, n° 3 (1989), pp. 519-549. Zbl0638.14011MR988101
  7. [7] Colliot-Thélène ( J.-L.), Sansuc ( J.-J.) et SIR SWINNERTON-DYER ( P.) . - Intersection of two quadrics and Châtelet surfaces, J. Reine Angew. Math.373 (1987), pp. 37-107; 374 (1987), pp. 72-168. Zbl0622.14029
  8. [8] Colliot-Thélène ( J.-L.) et Sansuc ( J.-J.) .— La descente sur les variétés rationnelles II, Duke Math. J.54 (1987), pp. 375-492. Zbl0659.14028MR899402
  9. [9] Colliot-Thélène ( J.-L.) et Sansuc ( J.-J.) .— On the Chow groups of certain rational surfaces : a sequel to a paper of S. BlochDuke Math.48 (1981), pp. 421-447. Zbl0479.14006MR620258
  10. [10] Harari ( D.) . — Méthode des fibrations et obstruction de Manin, Duke Math. J.75 (1994), pp. 221-260. Zbl0847.14001MR1284820
  11. [11] Manin ( Yu I.) .— Le groupe de Brauer-Grothendieck en géométrie diophantienne, in Actes du Congrès Intern. Math. (Nice 1970), Tome 1, Gauthiers-Villars, Paris1971, pp. 401-411. Zbl0239.14010MR427322
  12. [12] Nishimura ( H.) .— Some remark on rational points, Mem. Coll. Sci. Kyoto, Ser. A, 29 (1954), pp. 189-192. Zbl0068.14802MR95851
  13. [13] Salberger ( P.) .— Zero cycles on rational surfaces over number fields, Invent. Math.91 (1988), pp. 505-524. Zbl0688.14008MR928495
  14. [14] Salberger ( P.) . — Some new Hasse, principles for conic bundle surfaces, Séminaire de théorie des nombres de Paris 1987-1988, éd. C. Goldstein, Progress in Math.Birkhäuser81 (1989), pp. 283-305. Zbl0718.14013MR1042775
  15. [15] Sansuc ( J.-J.) .— Principe de Hasse, surfaces cubiques et intersections de deux quadriques, Journées arithmétiques de Besançon1985, Astérique147-148 (1987), pp. 183-207. Zbl0661.14021MR891428
  16. [16] Serre ( J.-P.) .— Corps Locaux, Hermann, Paris1968. Zbl0137.02601MR354618
  17. [17] Serre ( J.P.) .— Cours d'arithmétique, P.U.F., Paris1970. Zbl0225.12002MR255476
  18. [18] Skorobogatov ( A.N.) .— Arithmétic on certain quadric bundles of relative dimension 2, J. Reine Angew. Math.407 (1990), pp. 57-74. Zbl0692.14001MR1048528
  19. [19] Skorobogatov ( A.N.) — On the fibration method for proving the Hasse principle and weak approximation, Séminaire de théorie des nombres de Paris 1988-1989, éd. C. Goldstein, Progress in Math.Birkhäuser91 (1990), pp. 205-219. Zbl0748.14002MR1104707

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