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

How to cite

top

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

top
  1. [AV] Abramovich, D., Voloch, J.F.: Toward a proof of the Mordell-Lang conjecture in characteristic p, Duke Math. J.5 (1992) 103-115. Zbl0787.14026MR1162230
  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
  8. [Gie] Gieseker, D.: P-ample bundles and their Chern classes, Nagoya Math. J.43 (1971) 91-116. Zbl0221.14010MR296078
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.