Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-20T01:17:01.731Z Has data issue: false hasContentIssue false

On elliptic surfaces of Mordell-Weil rank 4

Published online by Cambridge University Press:  22 January 2016

Andrew Bremner*
Affiliation:
Arizona State University, Department of Mathematics, Tempe, Arizona 85287
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f: E→ P′(C) be an elliptic fibration with non-constant j-invariant, and possessing a section σ0. The group of sections of f is then naturally identified with the group of points defined over a function field C(u) of the generic fibre of f.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[ 1 ] Birch, B. J., Swinnerton-Dyer, H. P. F., Notes on elliptic curves II, J. reine angew. Math., 218 (1965), 79108.CrossRefGoogle Scholar
[ 2 ] Casseis, J. W. S., Ellison, W. J., Pfister, A., On sums of squares and on elliptic curves over function fields, J. Number Theory, 3 (1971), 125149.Google Scholar
[ 3 ] Cox, D. A., Zucker, S., Intersection numbers of sections of elliptic surfaces, Invent. Math., 53 (1979), 144.Google Scholar
[ 4 ] Kodaira, K., On compact analytic surfaces III, Ann. of Math., 78 (1963), 140.CrossRefGoogle Scholar
[ 5 ] Schwartz, C. F., A Mordell-Weil group of rank 8 and a subgroup of finite index, Nagoya Math. J., 93 (1984), 1926.Google Scholar
[ 6 ] Schwartz, C. F., On a family of elliptic surfaces with mordell-Weil rank 4, to appear.Google Scholar
[ 7 ] Shioda, T., On elliptic modular surfaces, J. Math. Soc. Japan, 24 (1972), 2057.CrossRefGoogle Scholar
[ 8 ] Swinnerton, H.-Dyer, P. F., The field of definition of the Néron-Severi group, Studies in Pure Mathematics, Hung. Acad, of Sci., Turan Memorial Volume, 1983.Google Scholar