Sur les conjectures de Mordell et Lang (d'après Vojta, Faltings et Bombieri)

Hindry, Marc

Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 39-56

MR Zbl | 2 citations dans Numdam

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     author = {Hindry, Marc},
     title = {Sur les conjectures de {Mordell} et {Lang} (d'apr\`es {Vojta,} {Faltings} et {Bombieri)}},
     booktitle = {Journ\'ees arithm\'etiques de Gen\`eve - 9-13 septembre 1991},
     editor = {Coray D. F. and P\'etermann Y.-F. S},
     series = {Ast\'erisque},
     pages = {39--56},
     year = {1992},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {209},
     mrnumber = {1211002},
     zbl = {0792.14009},
     language = {fr},
     url = {https://www.numdam.org/item/AST_1992__209__39_0/}
}

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Hindry, Marc. Sur les conjectures de Mordell et Lang (d'après Vojta, Faltings et Bombieri), dans Journées arithmétiques de Genève - 9-13 septembre 1991, Astérisque, no. 209 (1992), pp. 39-56. https://www.numdam.org/item/AST_1992__209__39_0/

Bibliographie
Cité par

[A-C-G-H] E. Arbarello, M. Cornalba, P. Griffiths and J. Harris. Geometry of curves, vol. I. Springer 1985. | MR | Zbl

[A-H] D. Abramovich and J. Harris. Abelian varieties and curves in $W_{d} C$ . Preprint. | Zbl | Numdam

[Bg] F. Bogomolov. Points of finite order on an abelian variety. Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980) | MR | Zbl

F. Bogomolov. Points of finite order on an abelian variety. AMS translation Math. USSR Izv. 17 (1981), 55-72. | Zbl | DOI

[B] E. Bombieri. The Mordell conjecture revisited. Ann. Scuola Norm. Sup. Pisa Ser. IV 17 (1990), 615-640 | MR | Zbl | EuDML | Numdam

E. Bombieri. The Mordell conjecture revisited. Ann. Scuola Norm. Sup. Pisa; errata ibid. 18 (1991), 473. | MR | Numdam | EuDML | Zbl

[Co-Si] G. Cornell and J. Silverman. Arithmetic geometry. Springer 1986. | MR | Zbl | DOI

[E-V] H. Esnault and E. Viehweg. Dyson's lemma for polynomials in several variables. Inv. Math. 78 (1984), 445-490. | MR | Zbl | EuDML | DOI

[F1] G. Faltings. Endlichkeitssätze für abelsche Varietäten über Zahlkörpern. Inv. Math. 73 (1983), 349-366. | MR | Zbl | EuDML | DOI

[F2] G. Faltings. Diophantine approximation on abelian varieties. Annals of Math. 133 (1991), 549-576. | MR | Zbl | DOI

[F3] G. Faltings. The general case of Lang's conjecture. Preprint. | MR | Zbl | DOI

[F4] G. Faltings. Preprint.

[Fr] G. Frey. A remark on isogenies of elliptic curves over quadratic fields. Compositio Math. 58 (1986), 133-134. | MR | Zbl | EuDML | Numdam

[G-S1] H. Gillet and G. Soulé. Un théorème de Riemann-Roch-Grothendieck arithmétique. C.R. Acad. Sci. Paris Sér. I Math. 309 (1989), 929-932. | MR | Zbl

[G-S2] H. Gillet and G. Soulé. Amplitude arithmétique. C.R. Acad. Sci. Paris Sér. I Math. 307 (1988), 887-890. | MR | Zbl

[G-S3] H. Gillet and G. Soulé. Arithmetic intersection theory. Publ. Math. IHES 72 (1990), 93-174. | MR | Zbl | EuDML | Numdam | DOI

[Ha1] R. Hartshorne. Algebraic geometry. Springer 1977. | MR | Zbl | DOI

[Ha2] R. Hartshorne. Ample subvarieties of algebraic varieties. Springer Lecture Notes in Math. 156 (1970). | MR | Zbl | EuDML

[Ha-Si] J. Harris and J. Silverman. Bielliptic curves and symmetric products. Proc. Amer. Math. Soc. 112 (1991), 347-356. | MR | Zbl | DOI

[H1] M. Hindry. Autour d'une conjecture de Serge Lang. Inv. Math. 94 (1988), 575-603. | MR | Zbl | EuDML | DOI

[H2] M. Hindry. Points quadratiques sur les courbes. C.R. Acad. Sci. Paris Sér. I Math. 305 (1987), 219-221. | MR | Zbl

[K-L] S. Kleiman and D. Laksov. Another proof of the existence of special divisors. Acta Math. 132 (1974), 163-176. | MR | Zbl | DOI

[La1] S. Lang. Fundamentals of diophantine geometry. Springer 1983. | MR | Zbl | DOI

[La2] S. Lang. Abelian varieties. Interscience, New York 1959. | MR

[La3] S. Lang. Integral points on curves. Publ. Math. IHES 6 (1960), 27-43. | MR | Zbl | EuDML | Numdam | DOI

[La4] S. Lang. Division points on curves. Ann. Mat. Pura Appl. (4) 70 (1965), 229-234. | MR | Zbl | DOI

[M1] D. Mumford. A remark on Mordell's conjecture. Amer. J. Math. 87 (1965), 1007-1016. | MR | Zbl | DOI

[M2] D. Mumford. Abelian varieties. Oxford University Press 1974. | Zbl

[R1] M. Raynaud. Courbes sur une variété abélienne et points de torsion. Inv. Math. 71 (1983), 207-233. | MR | Zbl | EuDML | DOI

[R2] M. Raynaud. Sous-variétés d'une variété abélienne et points de torsion. Arithmetic and geometry: papers dedicated to I.R. Shafarevich on the occasion of his sixtieth birthday, vol I, M. Artin and J. Tate ed., Birkhäuser 1983, 327-352. | MR | Zbl

[R3] M. Raynaud. Around the Mordell conjecture for function fields and a conjecture of Serge Lang. Algebraic geometry, Springer Lecture Notes 1016 (1983), 1-19. | MR | Zbl

[Ro] F. Roth Rational approximation to algebraic numbers. Mathematika 2 (1955), 1-20. | MR | Zbl

[Sch1] W. Schmidt. Diophantine approximation. Springer Lecture Notes 785 (1980). | MR | Zbl

[Sch2] W. Schmidt. Approximation to algebraic numbers. Enseign. Math. 17 (1971), 187-253. | MR | Zbl

[Se] J-P. Serre. Lectures on the Mordell-Weil theorem (translated by M. Brown from notes by M. Waldschmidt) . Vieweg 1989. | MR | Zbl

[Si] C. Siegel. Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. Phys. Math. Kl. (1929), 41-69. | JFM

[Sz1] L. Szpiro. Séminaire sur les pinceaux arithmétiques (la conjecture de Mordell). Astérisque 127 (1985). | MR | Zbl | Numdam

[Sz2] L. Szpiro. Sur les solutions d'un système d'équations polynomiales sur une variété abélienne (d'après Faltings et Vojta). Séminaire Bourbaki, exposé 729, Astérisque 189-190 (1990), 429-446. | MR | Zbl | EuDML | Numdam

[Vi] C. Viola. On Dyson's lemma. Ann. Scuola Norm. Sup. Pisa Ser. IV 12 (1985), 105-135. | MR | Zbl | EuDML | Numdam

[V1] P. Vojta. Siegel's theorem in the compact case. Annals of Math. 133 (1991), 509-548. | MR | Zbl | DOI

[V2] P. Vojta. Dyson's lemma on the product of two curves. Inv. Math. 98 (1989), 107-113. | Zbl | MR | EuDML | DOI

[V3] P. Vojta. Arithmetic discriminants and quadratic points on curves. Arithmetic algebraic geometry, Texel '89, Birkhäuser "Progress in Mathematics" 89 (1991), 356-376. | MR | Zbl

[V4] P. Vojta. A generalization of theorems of Faltings and Thue-Siegel-Roth-Wirsing. J. Amer. Math. Soc. 5 (1992), 763-804. | MR | Zbl | DOI

[W] A. Weil. Sur les courbes algébriques et les variétés qui s'en déduisent. Hermann, Paris 1948. | MR | Zbl