A flexible method for applying Chabauty's Theorem

Compositio Mathematica

Volumn 105, Issue 1, 1997, Pages 79-94

  Flynn, E V ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Chabauty; Curves; Formal groups; Jacobians; Rational points

Indexed keywords

EID: 0002439858     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1000111601294     Document Type: Article

References (17)

1. Cassels, J. W. S.: The Mordell-Weil group of curves of genus 2. Arithmetic and Geometry papers dedicated to I. R. Shafarevich on the occasion of his sixtieth birthday, Vol. 1. Arithmetic, 29-60, Birkhäuser, Boston (1983).
2. Cassels, J. W. S.: Arithmetic of curves of genus 2. Number Theory and Applications (ed. R.A. Mollin), 27-35. NATO ASI Series C, 265. Kluwer Academic Publishers, 1989.
3. Cassels, J. W. S.: Local Fields. London Mathematical Society Student Texts 3. Cambridge University Press, 1986.
4. Chabauty C.: Sur les points rationels des variétés algébriques dont l'irregularité et supérieur á la dimension. Comptes Rendus, Paris 212 (1941), 882-885.
5. Coleman, R. F.: Effective chabauty. Duke Math. J. 52 (1985), 765-780.
6. Flynn, E. V.: The Jacobian and formal group of a curve of genus 2 over an arbitrary ground field. Math. Proc. Comb. Phil Soc. 107 (1990), 425-441.
7. Flynn, E. V.: The group law on the Jacobian of a curve of genus 2. J. Reine Angew. Math. 439 (1993), 45-69.
8. Flynn, E. V.: Descent via isogeny on the Jacobian of a curve of genus 2. Acta Arithmetica LXVII.1 (1994), 23-43.
9. Flynn, E. V.: An explicit theory of heights in dimension 2. To appear in Trans. Amer. Math. Soc..
10. Flynn, E. V.: On a theorem of Coleman. Preprint, January 1995.
11. Gordon, D. M. and Grant, D.: Computing the Mordell-Weil rank of Jacobians of curves of genus 2. Trans. A.M.S., 337, Number 2, (1993), 807-824.
12. Grant, D.: Formal groups in genus 2. J. Reine Angew. Math. 411 (1990), 96-121.
13. Grant, D.: A curve for which Coleman's Chabauty bound is sharp. Preprint, 1993.
14. McCallum, W. G.: On the Shafarevich-Tate group of the Jacobian of a quotient of the Fermat curve. Invent. Math. 93 (1988), 637-666.
15. McCallum, W. G.: The arithmetic of Fermat curves. Math. Ann. 294 (1992), 503-511.
16. Schaefer, E. F.: 2-descent on the Jacobians of hyperelliptic curves. J. Number Theory (to appear).
17. Silverman, J. H.: The Arithmetic of Elliptic Curves. Springer-Verlag, New York (1986).