On large Picard groups and the Hasse Principle for curves and K3 surfaces
Daniel Coray ; Constantin Manoil
Acta Arithmetica, Tome 76 (1996), p. 165-189 / Harvested from The Polish Digital Mathematics Library
Publié le : 1996-01-01
EUDML-ID : urn:eudml:doc:206893
@article{bwmeta1.element.bwnjournal-article-aav76i2p165bwm,
     author = {Daniel Coray and Constantin Manoil},
     title = {On large Picard groups and the Hasse Principle for curves and K3 surfaces},
     journal = {Acta Arithmetica},
     volume = {76},
     year = {1996},
     pages = {165-189},
     zbl = {0877.14005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav76i2p165bwm}
}
Daniel Coray; Constantin Manoil. On large Picard groups and the Hasse Principle for curves and K3 surfaces. Acta Arithmetica, Tome 76 (1996) pp. 165-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav76i2p165bwm/

[000] [1] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves, I, J. Reine Angew. Math. 212 (1962), 7-25. | Zbl 0118.27601

[001] [2] A. Bremner, Algebraic points on quartic curves over function fields, Glasgow Math. J. 26 (1985), 187-190. | Zbl 0581.14015

[002] [3] A. Bremner, D. J. Lewis and P. Morton, Some varieties with points only in a field extension, Arch. Math. 43 (1984), 344-350. | Zbl 0532.14011

[003] [4] A. Brumer, Remarques sur les couples de formes quadratiques, C. R. Acad. Sci. Paris A 286 (1978), 679-681. | Zbl 0392.10021

[004] [5] J. W. S. Cassels, The arithmetic of certain quartic curves, Proc. Roy. Soc. Edinburgh 100 (1985), 201-218. | Zbl 0589.14029

[005] [6] J. W. S. Cassels, Local Fields, Cambridge Univ. Press, Cambridge, 1986.

[006] [7] J. W. S. Cassels and A. Fröhlich (ed.), Algebraic Number Theory, Academic Press, London, 1967.

[007] [8] J. W. S. Cassels and M. J. T. Guy, On the Hasse principle for cubic surfaces, Mathematika 13 (1966), 111-120. | Zbl 0151.03405

[008] [9] F. Châtelet, Variations sur un thème de Poincaré, Ann. Ecole Norm. Sup. 61 (1944), 249-300. | Zbl 0063.00801

[009] [10] J.-L. Colliot-Thélène, Les grands thèmes de François Châtelet, Enseign. Math. 34 (1988), 387-405. | Zbl 0678.01008

[010] [11] J.-L. Colliot-Thélène, D. Coray et J.-J. Sansuc, Descente et principe de Hasse pour certaines variétés rationnelles, J. Reine Angew. Math. 320 (1980), 150-191. | Zbl 0434.14019

[011] [12] J.-L. Colliot-Thélène et J.-J. Sansuc, La descente sur les variétés rationnelles, II, Duke Math. J. 54 (1987), 375-492. | Zbl 0659.14028

[012] [13] J.-L. Colliot-Thélène, J.-J. Sansuc and Sir P. Swinnerton-Dyer, Intersections of two quadrics and Châtelet surfaces, J. Reine Angew. Math. 373 (1987), 37-107; 374 (1987), 72-168.

[013] [14] J.-L. Colliot-Thélène et A. N. Skorobogatov, Groupe de Chow des zéro-cycles sur les fibrés en quadriques, K-Theory 7 (1993), 477-500. | Zbl 0837.14002

[014] [15] J.-L. Colliot-Thélène and Sir P. Swinnerton-Dyer, Hasse principle and weak approximation for pencils of Severi-Brauer and similar varieties, J. Reine Angew. Math. 453 (1994), 49-112. | Zbl 0805.14010

[015] [16] D. Coray, Arithmetic on cubic surfaces, Ph.D. thesis, Trinity College, Cambridge, 1974, 66 pp. | Zbl 0337.14028

[016] [17] D. Coray, Algebraic points on cubic hypersurfaces, Acta Arith. 30 (1976), 267-296. | Zbl 0294.14012

[017] [18] D. Coray, On a problem of Pfister about intersections of three quadrics, Arch. Math. 34 (1980), 403-411. | Zbl 0426.14008

[018] [19] D. Coray, A remark on systems of quadratic forms, in: Math. Forschungsinstitut Oberwolfach, Tagungsbericht 22/1981: Quadratische Formen, 18.5-23.5.1981, 8-9.

[019] [20] D. Coray and M. A. Tsfasman, Arithmetic on singular Del Pezzo surfaces, Proc. London Math. Soc. 57 (1988), 25-87. | Zbl 0653.14018

[020] [21] P. Deligne, Les conjectures de Weil, I, Publ. Math. I.H.E.S. 43 (1974), 273-307.

[021] [22] W. Fulton, Intersection Theory, Springer, Berlin, 1984. | Zbl 0541.14005

[022] [23] A. Grothendieck, Le groupe de Brauer, III, Exemples et compléments, in: Dix exposés sur la cohomologie des schémas, North-Holland, Amsterdam, 1968.

[023] [24] R. Hartshorne, Algebraic Geometry, Springer, New York, 1977.

[024] [25] D. Husemöller, Elliptic Curves, Springer, New York, 1987.

[025] [26] D. Kanevsky, Application of the conjecture on the Manin obstruction to various diophantine problems, Journées Arithmétiques de Besançon, Astérisque 147-148 (1987), 307-314. | Zbl 0625.14010

[026] [27] B. È. Kunyavskiĭ, A. N. Skorobogatov and M. A. Tsfasman, Del Pezzo surfaces of degree four, Suppl. Bull. Soc. Math. France 117 (2) (1989), Mémoire no. 37, 112 pp. | Zbl 0705.14039

[027] [28] S. Lang and A. Weil, Number of points of varieties in finite fields, Amer. J. Math. 76 (1954), 819-827. | Zbl 0058.27202

[028] [29] S. Lichtenbaum, Duality theorems for curves over p-adic fields, Invent. Math. 7 (1969), 120-136. | Zbl 0186.26402

[029] [30] Yu. I. Manin, Cubic Forms, Nauka, Moscow, 1972 (in Russian); English transl.: North-Holland, Amsterdam, 1980.

[030] [31] C. Manoil, Courbes sur une surface K3, thèse, Univ. Genève, 1992, 107 pp.

[031] [32] A. S. Merkurjev and J.-P. Tignol, The multipliers of similitudes and the Brauer group of homogeneous varieties, preprint, Univ. Cath. Louvain, 1994, 30 pp. | Zbl 0819.16015

[032] [33] J. S. Milne, Étale Cohomology, Princeton Univ. Press, Princeton, N.J., 1980.

[033] [34] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969.

[034] [35] D. Mumford, Lectures on Curves on an Algebraic Surface, Princeton Univ. Press, Princeton, N.J., 1966. | Zbl 0187.42701

[035] [36] P. Samuel, Anneaux factoriels, Inst. Pesq. Mat., Univ. S ao Paulo, 1963. | Zbl 0123.03303

[036] [37] P. Samuel, About Euclidean rings, J. Algebra 19 (1971), 282-301. | Zbl 0223.13019

[037] [38] J.-P. Serre, Corps locaux, Hermann, Paris, 1962.

[038] [39] J.-P. Serre, Cours d'arithmétique, Presses Univ. France, Paris, 1970.

[039] [40] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986. | Zbl 0585.14026

[040] [41] T. A. Springer, Sur les formes quadratiques d'indice zéro, C. R. Acad. Sci. Paris 234 (1952), 1517-1519. | Zbl 0046.24303

[041] [42] T. A. Springer, Quadratic forms over fields with a discrete valuation, Indag. Math. 17 (1955), 352-362.

[042] [43] V. E. Voskresenskiĭ, Algebraic Tori, Nauka, Moscow, 1977 (in Russian).

[043] [44] E. Witt, Über ein Gegenbeispiel zum Normensatz, Math. Z. 39 (1935), 462-467. | Zbl 0010.14901