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

• Autorzy: E. V. Flynn , N. P. Smart
• Języki publikacji: EN

Kategorie tematyczne

• 11G30: Curves of arbitrary genus or genus ≠ 1 over global fields
• 14H40: Jacobians, Prym varieties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 79
• Numer: 4
• Strony: 333-352

Daty

wydano

1997

otrzymano

1996-06-28

poprawiono

1996-12-02

Twórcy

autor

E. V. Flynn

• Department of Pure Mathematics, Liverpool University, P.O. Box 147, Liverpool, L69 3BX, U.K.

autor

N. P. Smart

• 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.