Weak approximation and non-abellian fundamental groups

 Access to full text

 Full (PDF)

1. [1] BARTH W., PETERS C., VAN DE VEN A., Compact Complex Surfaces, Ergeb. der Math. und ihr. Grenzgeb., 3. Folge, Vol. 4, Springer, Berlin, 1984. Zbl0718.14023MR86c:32026
2. [2] BEAUVILLE A., Surfaces algébriques complexes, Astérisque, Vol. 54, Soc. Math. Fr., Paris, 1978. Zbl0394.14014MR58 #5686
3. [3] BOGOMOLOV F.A., TSCHINKEL Y., On the density of rational points on elliptic fibrations, Preprint, 1998. Zbl0957.14016
4. [4] BOGOMOLOV F.A., TSCHINKEL Y., Density of rational points on Enriques surfaces, Preprint, 1998. Zbl0957.14016MR99m:14040
5. [5] COLLIOT-THÉLÈNE J.-L., SANSUC J.-J., La descente sur les variétés rationnelles II, Duke Math. J. 54 (1987) 375-492. Zbl0659.14028MR89f:11082
6. [6] COLLIOT-THÉLÈNE J.-L., SKOROBOGATOV A.N., SIR SWINNERTON-DYER P., Double fibres and double covers : paucity of rational points, Acta Arithmetica 79 (2) (1997) 113-135. Zbl0863.14011MR98a:11081
7. [7] DEMAILLY J.-P., PETERNELL T., SCHNEIDER M., Compact complex manifolds with numerically effective tangent bundles, J. Algebraic Geometry 3 (1994) 295-345. Zbl0827.14027MR95f:32037
8. [8] DOLGACHEV I., Algebraic surfaces with q = pg = 0, in : Algebraic Surfaces, C.I.M.E., III ciclo, 1977. 
9. [9] EKEDAHL T., An effective version of Hilbert's irreducibility theorem, in : Goldstein C. (Ed.), Séminaire de Théorie des Nombres de Paris 1988-1989, Progress in Math., Vol. 91, Birkhäuser, 1990, pp. 241-248. Zbl0729.12005MR92f:14018
10. [10] FREY G., JARDEN M., Approximation theory and the rank of abelian varieties over large algebraic fields, Proc. London Math. Soc. 28 (3) (1974) 112-128. Zbl0275.14021MR49 #2765
11. [11] GROTHENDIECK A., DIEUDONNÉ J., Étude cohomologique des faisceaux cohérents (EGA3), I.H.E.S., Publ. Math. 11 (1961). 
12. [12] GROTHENDIECK A., Revêtements étales et groupe fondamental (SGA1), Lecture Notes in Mathematics, Vol. 224, Springer, 1971. Zbl0234.14002MR50 #7129
13. [13] GROTHENDIECK A., Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA2), Adv. Studies in Pure Math., Masson-North-Holland, Paris, Amsterdam, 1968. Zbl0197.47202MR57 #16294
14. [14] GROTHENDIECK A., Le groupe de Brauer, II, in : Dix Exposés sur la Cohomologie des Schémas, Masson-North-Holland, Amsterdam, 1968. Zbl0198.25803MR39 #5586b
15. [15] GROTHENDIECK A., Le groupe de Brauer, III, in : Dix Exposés sur la Cohomologie des Schémas, Masson-North-Holland, Amsterdam, 1968. Zbl0198.25901MR39 #5586b
16. [16] HARARI D., SKOROBOGATOV A.N., Non-abelian cohomology and rational points, Prépublication I.H.E.S., 1999. 
17. [17] HARRIS J., TSCHINKEL Y., Rational points on quartics, Preprint, 1998. Zbl0982.14013
18. [18] HARTSHORNE R., Algebraic Geometry, Springer, New York, 1977. Zbl0367.14001MR57 #3116
19. [19] KEUM J.H., Every algebraic Kummer surface is the K3-cover of an Enriques surface, Nagoya Math. J. 118 (1990) 99-110. Zbl0699.14047MR91f:14036
20. [20] KNESER M., Starke Approximation in algebraischen Gruppen, I, J. Reine Angew. Math. 218 (1965) 190-203. Zbl0143.04701MR32 #2416
21. [21] KOLLÁR J., Shafarevich Maps and Automorphic Forms, Princeton University Press, 1995. Zbl0871.14015MR96i:14016
22. [22] LANG S., Abelian Varieties, Interscience Tracts in Pure and Appl. Math., Vol. 7, Interscience, New York, 1959. Zbl0098.13201MR21 #4959
23. [23] LANG S., Algebraic Number Theory, Springer, New York, 1986. Zbl0601.12001
24. [24] LANG S., NÉRON A., Rational points of abelian varieties over function fields, Amer. J. Math. 81 (1959) 95-118. Zbl0099.16103MR21 #1311
25. [25] MANIN YU.I., Le groupe de Brauer-Grothendieck en géométrie diophantienne, in : Actes du Congrès Intern. Math. (Nice 1970), Tome 1, Gauthiers-Villars, Paris, 1971, pp. 401-411. Zbl0239.14010
26. [26] MATSUMURA H., Commutative Algebra, W. A. Benjamin Co., New York, 1980. Zbl0211.06501MR82i:13003
27. [27] MILNE J.S., Étale Cohomology, Princeton University Press, Princeton, NJ, 1980. Zbl0433.14012MR81j:14002
28. [28] MINCHEV KH.P., Strong approximation for varieties over algebraic number fields, Dokl. Akad. Nauk BSSR 33 (1) (1989) 5-8 (Russian). Zbl0693.14001MR90a:11065
29. [29] MUMFORD D., Abelian Varieties, Tata Institute of Fundamental Research, Oxford University Press, Bombay, 1970. Zbl0223.14022MR44 #219
30. [30] SARNAK P., WANG L., Some hypersurfaces in P4 and the Hasse principle, C. R. Acad. Sci. Paris 321 (1995) 319-322. Zbl0857.14013MR96j:14014
31. [31] SERRE J.-P., Sur la topologie des variétés algébriques en caractéristique p, in : Symposium Internacional de Topologia Algebraica, Mexico, 1958, pp. 24-53. Zbl0098.13103MR20 #4559
32. [32] SKOROBOGATOV A.N., Beyond the Manin obstruction, Invent. Math. 135 (1999) 399-424. Zbl0951.14013MR2000c:14022
33. [33] WANG L., Brauer-Manin obstruction to weak approximation on abelian varieties, Israel J. Math. 94 (1996) 189-200. Zbl0870.14032MR97e:11069

1. Yongqi Liang, Arithmetic of 0-cycles on varieties defined over number fields
2. Emmanuel Peyre, Obstructions au principe de Hasse et à l’approximation faible