Courbes algébriques de genre ≥ 2 possédant de nombreux points rationnels

Leopoldo Kulesz

Acta Arithmetica (1998)

  • Volume: 87, Issue: 2, page 103-120
  • ISSN: 0065-1036

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Leopoldo Kulesz. "Courbes algébriques de genre ≥ 2 possédant de nombreux points rationnels." Acta Arithmetica 87.2 (1998): 103-120. <http://eudml.org/doc/207207>.

@article{LeopoldoKulesz1998,
author = {Leopoldo Kulesz},
journal = {Acta Arithmetica},
keywords = {genus ; hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; families of curves},
language = {fre},
number = {2},
pages = {103-120},
title = {Courbes algébriques de genre ≥ 2 possédant de nombreux points rationnels},
url = {http://eudml.org/doc/207207},
volume = {87},
year = {1998},
}

TY - JOUR
AU - Leopoldo Kulesz
TI - Courbes algébriques de genre ≥ 2 possédant de nombreux points rationnels
JO - Acta Arithmetica
PY - 1998
VL - 87
IS - 2
SP - 103
EP - 120
LA - fre
KW - genus ; hyperelliptic involution; group of automorphisms of a curve; elliptic curves; isogenies; many rational points; algebraic curve; families of curves
UR - http://eudml.org/doc/207207
ER -

References

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  1. [A-M] A. O. L. Atkin and F. Morain, Finding suitable curves for the Elliptic Curve Method of factorization, Math. Comp. 60 (1993), 399-405. 
  2. [CHM1] L. Caporaso, J. Harris and B. Mazur, Uniformity of rational points, J. Amer. Math. Soc. 10 (1997), 1-35. Zbl0872.14017
  3. [CHM2] L. Caporaso, J. Harris and B. Mazur, How many rational points can a curve have?, dans: The Moduli Space of Curves (Texel Island, 1994), Progr. Math. 129, Birkhäuser, 1995, 13-31. 
  4. [C-F] J. W. S. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, London Math. Soc. Lecture Note Ser. 230, Cambridge Univ. Press, 1996. Zbl0857.14018
  5. [Dix] J. Dixmier, On the projective invariant of quartic plane curves, Adv. Math. 64 (1987), 279-304. Zbl0668.14006
  6. [EGH] D. Eisenbud, M. Green and J. Harris, Cayley-Bacharach theorems and conjectures, Bull. Amer. Math. Soc. 33 (1996), 295-324. Zbl0871.14024
  7. [Elk1] N. Elkies, Curves with many points, preprint, 1995. 
  8. [Elk2] N. Elkies, Communication personnelle, 1997. 
  9. [K-K] W. Keller et L. Kulesz, Courbes algébriques de genre 2 et 3 possédant de nombreux points rationnels, C. R. Acad. Sci. Paris Sér. I 321 (1995), 1469-1472. Zbl0873.11038
  10. [Kul] L. Kulesz, Courbes algébriques de genre 2 possédant de nombreux points rationnels, ibid., 91-94. 
  11. [Lep] F. Leprévost, Familles de courbes hyperelliptiques, dans : Séminaire de Théorie des nombres, Paris, 1991-1992, S. David (ed.), Progr. Math. 116, Birkhäuser, 1993, 107-119. 
  12. [Maz] B. Mazur, Rational isogenies of prime degree, Invent. Math. 44 (1978), 129-169. 
  13. [Mes] J.-F. Mestre, Construction explicite de courbes de genre 2 à partir de leurs modules, dans : Effective Methods in Algebraic Geometry, Progr. Math. 94, Birkhäuser, 1991, 313-334. 
  14. [Sta] C. Stahlke, Algebraic curves over Q with many rational points and minimal automorphism group, Internat. Math. Res. Notices 1997, no. 1, 1-4. Zbl0881.14009
  15. [Suy] H. Suyama, Informal preliminary report (8), 1985. 
  16. [Vel] J. Vélu, Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris Sér. A 273 (1971), 238-241. 

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