Lang’s conjecture in characteristic p : an explicit bound

Alexandru Buium; José Felipe Voloch

Compositio Mathematica (1996)

  • Volume: 103, Issue: 1, page 1-6
  • ISSN: 0010-437X

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Buium, Alexandru, and Voloch, José Felipe. "Lang’s conjecture in characteristic $p$ : an explicit bound." Compositio Mathematica 103.1 (1996): 1-6. <http://eudml.org/doc/90459>.

@article{Buium1996,
author = {Buium, Alexandru, Voloch, José Felipe},
journal = {Compositio Mathematica},
keywords = {finiteness theorem; function field of characteristic ; Mordell's conjecture; Manin-Mumford conjecture; Lang's conjecture},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Kluwer Academic Publishers},
title = {Lang’s conjecture in characteristic $p$ : an explicit bound},
url = {http://eudml.org/doc/90459},
volume = {103},
year = {1996},
}

TY - JOUR
AU - Buium, Alexandru
AU - Voloch, José Felipe
TI - Lang’s conjecture in characteristic $p$ : an explicit bound
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 103
IS - 1
SP - 1
EP - 6
LA - eng
KW - finiteness theorem; function field of characteristic ; Mordell's conjecture; Manin-Mumford conjecture; Lang's conjecture
UR - http://eudml.org/doc/90459
ER -

References

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  2. [B1] Buium, A.: Intersections in jet spaces and a conjecture of Lang, S.Annals of Math.136 (1992) 557-567. Zbl0817.14021MR1189865
  3. [B2] Buium, A.: Geometry of differential polynomial functions I: algebraic groups, Amer. J. Math.115,6 (1993) 1385-1444. Zbl0797.14016MR1254738
  4. [B3] Buium, A.: Geometry of differential polynomial functions II: algebraic curves, Amer. J. Math., to appear. Zbl0829.14018MR1287940
  5. [B4] Buium, A.: Effective bound for the geometric Lang conjecture, Duke Math. J.71, 2 (1993) 475-499. Zbl0812.14029MR1233446
  6. [F] Faltings, G.: Endlichkeitsatze für abelsche varietäten über Zahlkorpern, Invent: Math.73 (1983) 349-366. Zbl0588.14026MR718935
  7. [Fu] Fulton, W.: Intersection Theory, Springer1984. Zbl0541.14005MR732620
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  9. [Gra] Grauert, H.: Mordell's Vermutung über rationale Punkte auf algebraische Kurven und Functionenkorper, Publ. Math. IHES25 (1965). Zbl0137.40503MR222087
  10. [L] Lang, S.: Division points on curves, Ann. Mat. Pura Appl. (4) 70 (1965) 229-234. Zbl0151.27401MR190146
  11. [Man] Manin, Yu.: Rational points on algebraic curves over function fields, Izvestija Akad Nauk SSSR, Mat. Ser. t. 27 (1963) 1395-1440. Zbl0178.55102MR157971
  12. [MD] Martin-Deschamps, M.: Propriétés de descente des variétés a fibre cotangent ample, Ann. Inst. Fourier, 34, 3 (1984) 39-64. Zbl0535.14013MR762693
  13. [Maz] Mazur, B.: Arithmetic on curves, Bull. Amer. Math. Soc.14, 2 (1986) 207-259. Zbl0593.14021MR828821
  14. [Mum] Mumford, D.: Abelian varieties, Oxford Univ. Press1974. Zbl0326.14012
  15. [R] Raynaud, M.: Courbes sur une variété abélienne et points de torsion, Invent. Math.71 (1983) 207-235. Zbl0564.14020MR688265
  16. [Ro] Rosenlicht, M.: Extensions of vector groups by abelian varieties, Am. J. of Math.80 (1958) 685-714. Zbl0091.33303MR99340
  17. [Sa] Samuel, P.: Compléments a un article de Hans Grauert sur la conjecture de Mordell, Publ. Math. IHES29 (1966) 55-62. Zbl0144.20102MR204430
  18. [Sz] Szpiro, L.: Propriétés numériques du faisceau dualisant relatif, Astérisque86 (1981) 44-78. Zbl0517.14006
  19. [T] Tango, H.: On the behaviour of extensions of vector bundles under the Frobenius map, Nagoya Math. J.48 (1972) 73-89. Zbl0239.14007MR314851
  20. [V] Voloch, J.F.: On the conjectures of Mordell and Lang in positive characteristic, Invent. Math.104 (1991) 643-646. Zbl0735.14019MR1106753

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