The density of rational and integral points on algebraic varieties
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 25 (1992) no. 2, pp. 135-178. 
@article{ASENS_1992_4_25_2_135_0,
     author = {Brown, M. L.},
     title = {The density of rational and integral points on algebraic varieties},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {135--178},
     publisher = {Elsevier},
     volume = {Ser. 4, 25},
     number = {2},
     year = {1992},
     doi = {10.24033/asens.1646},
     mrnumber = {94d:11041},
     zbl = {0764.14013},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1646/}
}
TY  - JOUR
AU  - Brown, M. L.
TI  - The density of rational and integral points on algebraic varieties
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1992
SP  - 135
EP  - 178
VL  - 25
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.24033/asens.1646/
DO  - 10.24033/asens.1646
LA  - en
ID  - ASENS_1992_4_25_2_135_0
ER  - 
%0 Journal Article
%A Brown, M. L.
%T The density of rational and integral points on algebraic varieties
%J Annales scientifiques de l'École Normale Supérieure
%D 1992
%P 135-178
%V 25
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.24033/asens.1646/
%R 10.24033/asens.1646
%G en
%F ASENS_1992_4_25_2_135_0
Brown, M. L. The density of rational and integral points on algebraic varieties. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 25 (1992) no. 2, pp. 135-178. doi : 10.24033/asens.1646. http://www.numdam.org/articles/10.24033/asens.1646/

[1] D. Barlet, Développements asymptotiques des fonctions obtenues par intégration sur les fibres (Invent. Math., Vol. 68, 1982, pp. 129-174). | MR | Zbl

[2] D. Bertrand, Lemmes de zéros et nombres transcendants (Séminaire Bourbaki, No. 652, 1985/1986 ; Astérisque, Vol. 145-146, 1987, pp. 21-44). | Numdam | MR | Zbl

[3] F. A. Bogomolov, Points of Finite Order on an Abelian Variety [Izv. Akad. Nauk C.C.C.P., Vol. 44, 1980 (= Math. U.S.S.R. Izv., Vol. 17, 1981, pp. 55-72). | Zbl

[4] N. Bourbaki, Groupes et Algèbres de Lie, Herman, Paris, 1971.

[5] M. L. Brown, Schémas en groupes et lemmes de zéros (Publ. Math. Paris-VI, Problèmes Diophantiens, 1984/1985).

[6] M. L. Brown, Remark on two Diophantine Conjectures (Bull. L.M.S., Vol. 67, 1985, pp. 391-392). | MR | Zbl

[7] M. L. Brown, Endomorphisms of Group Schemes and Rational Points on Curves (Bull. Soc. Math. France, Vol. 115, 1987, pp. 1-17). | Numdam | MR | Zbl

[8] M. L. Brown, Zero Estimates for Polynomials Over Commutative Rings (Math. Annalen, Vol. 272, 1985, pp. 489-504). | MR | Zbl

[9] M. L. Brown, Construction de hauteurs locales et globales sur les variétés algébriques (C. R. Acad. Sci. Paris, T. 307, Series I, 1988, pp. 87-90). | MR | Zbl

[10] M. L. Brown, The Tame Fundamental Group of an Abelian Variety and Integral Points (Compositio Math., Vol. 72, 1989, pp. 1-31). | Numdam | MR | Zbl

[11] G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern (Invent. Math., Vol. 73, 1983, pp. 349-366). | MR | Zbl

[12] G. Faltings, Diophantine Approximation on Abelian Varieties (Annals Math., Vol. 133, 1991, pp. 549-576). | MR | Zbl

[13] J. Franke, Yu. I. Manin and Yu. Tschinkel, Rational Points of Bounded Height on Fano Varieties (Invent. Math., Vol. 95, 1989, pp. 421-435). | MR | Zbl

[14] H. Furstenberg, Recurrence in Ergodic theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, 1981. | MR | Zbl

[15] A. Grothendieck, Schémas en Groupes (SGA 3), I, II, III (Lect. Notes Math., Nos. 151, 152, 153, Springer Verlag, Berlin-Heidelberg-New York, 1970). | MR

[16] A. Grothendieck and J. Dieudonné, Éléments de Géométrie Algébrique, I.H.E.S. Publ. Math., 1960-1967. | Numdam

[17] G. H. Hardy and E. M. Wright, Introduction to the Theory of Numbers, 3rd Edition, Oxford University Press, Oxford, 1954. | MR | Zbl

[18] M. Hindry, Autour d'une conjecture de Serge Lang (Invent. Math., Vol. 94, 1988, pp. 575-603). | MR | Zbl

[19] J.-I. Igusa, Some Observations on Higher Degree Characters (Am. J. Math., Vol. 99, 1977, pp. 393-417). | MR | Zbl

[20] S. Iitaka, On Logarithmic Kodaira Dimension of Algebraic Varieties, in Complex Analysis and Algebraic Geometry, a collection of papers dedicated to K. Kodaira, pp. 175-190, Cambridge Univ. Press, Cambridge, 1977. | MR | Zbl

[21] S. Iitaka, Algebraic Geometry (Graduate Texts Math., Vol. 76, Springer Verlag, Berlin-Heidelberg-New York, 1982). | MR | Zbl

[22] S. Iitaka, Birational Geometry and Logarithmic Forms, in Recent Progress in Algebraic Geometry in Japan, M. NAGATA Ed., North Holland/Kinokuniya, Tokyo, 1983. | MR | Zbl

[23] S. Lang, Abelian Varieties, Interscience Publ., New York, 1959. | MR | Zbl

[24] S. Lang, Fundamentals of Diophantine Geometry, Springer Verlag, Berlin-Heidelberg-New York, 1978.

[25] S. Lang, Algebraic Number Theory, Addison Wesley, Reading Mass., 1970. | MR | Zbl

[26] M. Laurent, Equations diophantiennes exponentielles (Invent. Math., Vol. 78, 1984, pp. 299-327). | MR | Zbl

[27] H. M. Maire, Sur les distributions images réciproques par une fonction analytique (Comment. Math. Helvetici, Vol. 51, 1976, pp. 395-410). | MR | Zbl

[28] D. W. Masser, On Polynomials and Exponential Polynomials in Several Complex Variables (Invent. Math., Vol. 63, 1981, pp. 81-95). | MR | Zbl

[29] D. W. Masser, Small Values of the Quadratic Part of the Néron-Tate Height (Compositio Math., Vol. 53, 1986, pp. 153-170). | Numdam | MR | Zbl

[30] D. W. Masser and G. Wüstholz, Zero Estimates on Group Varieties I (Invent. Math., Vol. 64, 1981, pp. 489-516). | MR | Zbl

[31] B. Mazur, Modular Curves and the Eisenstein Ideal (I.H.E.S. Publ. Math., No. 47, 1977, pp. 33-186). | Numdam | MR | Zbl

[32] D. Mumford, A Remark on Mordell's Conjecture (Am. J. Math., Vol. LXXXVII, 1965, pp. 1007-1016). | MR | Zbl

[33] A. Néron, Quasi-fonctions et hauteurs sur les variétés algébriques (Annals Math., Vol. 82, 1965, pp. 249-331). | MR | Zbl

[34] J. Oesterlé, Réduction modulo pn des sous-ensembles analytiques fermés de Zp (Invent. Math., Vol. 66, 1982, pp. 325-341). | MR | Zbl

[35] A. Ogg, Modular Forms and Dirichlet Series, W. A. Benjamin, New York, 1969. | Zbl

[36] P. Philippon, Lemmes de zéros dans les groupes algébriques commutatifs (Bull. Soc. Math. France, Vol. 114, 1986, pp. 355-383). | Numdam | MR | Zbl

[37] M. Raynaud, Faisceaux amples sur les schémas en groupes et les espaces homogènes (Lect. Notes Math., No. 119, Springer Verlag, Heidelberg, 1970). | MR | Zbl

[38] M. Raynaud, Sous-variétés d'une variété abélienne et points de torsion, in Arithmetic and Geometry (Prog. in Math. Birkhäuser, Vol. 35, 1983, pp. 327-352). | MR | Zbl

[39] M. Raynaud, Around the Mordell Conjecture for Function Fields and a Conjecture of Lang, in Algebraic Geometry, Tokyo and Kyoto, 1982 (Lect. Notes Math., No. 1016, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1983). | Zbl

[40] P. Samuel, Compléments à un article de Hans Grauert sur la conjecture de Mordell (I.H.E.S. Publ. Math., Vol. 29, 1966, pp. 55-62). | Numdam | MR | Zbl

[41] J.-P. Serre, Quelques applications du théorème de densité de Chebotarev (I.H.E.S. Publ. Math., Vol. 54, 1981, pp. 123-201). | Numdam | MR | Zbl

[42] J.-P. Serre, Résumé des cours et travaux (Annuaire du Collège de France, 1985-1986, pp. 95-100).

[43] J.-P. Serre, Lectures on The Mordell-Weil Theorem, Vieweg, Braunschweig/Wiesbaden, 1989. | MR | Zbl

[44] J. Silverman, The Arithmetic of Elliptic Curves (Graduate Texts in Math., Vol. 106, Springer Verlag, Berlin-Heidelberg-New York-Tokyo, 1986). | MR | Zbl

[45] J. Silverman, Integral Points on Abelian Varieties are Widely Spaced (Compositio Math., Vol. 61, 1987, pp. 253-266). | Numdam | MR | Zbl

[46] L. Szpiro, Sur les solutions d'un système d'équations polynomiales sur une variété abélienne (d'après G. Faltings and P. Vojta) (Séminaire N. Bourbaki, No. 729, June 1990). | Numdam | Zbl

Cité par Sources :