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1997 | 79 | 4 | 333-352
Tytuł artykułu

Canonical heights on the Jacobians of curves of genus 2 and the infinite descent

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
79
Numer
4
Strony
333-352
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-06-28
poprawiono
1996-12-02
Twórcy
autor
  • Department of Pure Mathematics, Liverpool University, P.O. Box 147, Liverpool, L69 3BX, U.K.
autor
  • Institute of Mathematics and Statistics, University of Kent at Canterbury, Canterbury, Kent, CT2 7NF, U.K.
Bibliografia
  • [1] J. W. S. Cassels, Lectures on Elliptic Curves, London Math. Soc. Stud. Texts 24, Cambridge University Press, 1991.
  • [2] J. W. S. Cassels and E. V. Flynn, Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2, Cambridge University Press, 1996.
  • [3] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992.
  • [4] E. V. Flynn, The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field, Proc. Cambridge Philos. Soc. 107 (1990), 425-441.
  • [5] E. V. Flynn, The group law on the Jacobian of a curve of genus 2, J. Reine Angew. Math. 439 (1993), 45-69.
  • [6] E. V. Flynn, Descent via isogeny in dimension 2, Acta Arith. 66 (1994), 23-43.
  • [7] E. V. Flynn, An explicit theory of heights, Trans. Amer. Math. Soc. 347 (1995), 3003-3015.
  • [8] E. V. Flynn, B. Poonen, and E. F. Schaefer, Cycles of quadratic polynomials and rational points on a genus 2 curve, preprint, 1996.
  • [9] B. Gross, Local heights on curves, in: Arithmetic Geometry, G. Cornell and J. H. Silverman (eds.), Springer, 1986, 327-339.
  • [10] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
  • [11] M. Pohst and H. Zassenhaus, Algorithmic Algebraic Number Theory, Cambridge University Press, 1989.
  • [12] E. F. Schaefer, 2-descent on the Jacobians of hyperelliptic curves, J. Number Theory 51 (1995), 219-232.
  • [13] E. F. Schaefer, Class groups and Selmer groups, J. Number Theory 56 (1996), 79-114.
  • [14] S. Siksek, Infinite descent on elliptic curves, Rocky Mountain J. Math. 25 (1995), 1501-1538.
  • [15] J. H. Silverman, The Arithmetic of Elliptic Curves, Springer, 1986.
  • [16] J. H. Silverman, Computing heights on elliptic curves, Math. Comp. 51 (1988), 339-358.
  • [17] J. H. Silverman, The difference between the Weil height and the canonical height on elliptic curves, Math. Comp. 55 (1990), 723-743.
  • [18] J. H. Silverman, Advanced Topics in the Arithmetic of Elliptic Curves, Springer, 1994.
  • [19] J. H. Silverman, Computing canonical heights with little (or no) factorization, preprint, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav79i4p333bwm
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