Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T12:34:42.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Simple Factors in the Jacobian of a Fermat Curve

Published online by Cambridge University Press:  20 November 2018

Neal Koblitz  and
David Rohrlich
Neal Koblitz
Affiliation:
Harvard University, Cambridge, Massachusetts
David Rohrlich
Affiliation:
Harvard University, Cambridge, Massachusetts
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

denote the Nth Fermat curve. The period lattice of F(N) is contained with finite index in the product of certain lattices Lr,s (see [6]), and to this inclusion of lattices there corresponds an isogeny of the Jacobian of F(N) onto a product of abelian varieties. The purpose of this paper is to determine when two factors in this product are isogenous over C, and whether they are absolutely simple.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1183 - 1205
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Carlitz, L. and Olson, F. R., Maillet1 s determinant, Proc. Amer. Math. Soc. G (1955), 265–269.Google Scholar
2. Iwasawa, K., Lectures on p-adic L-functions, Annals of Math. Studies 74, Princeton, 1972.Google Scholar
3. Kac, M., Statistical independence in probability, analysis, and number theory (John Wiley and Sons, New York, 1959).Google Scholar
4. Kubert, D. and Lang, S., Distributions on toroidal groups, Math. Zeit. 148 (1976), 33–51.Google Scholar
5. Lang, S., Cyclotomic fields (Springer-Verlag, New York, 1978).Google Scholar
6. Rohrlich, D., Periods of the Fermât curve, Appendix to Gross, B., On the periods of abelian integrals and a formula of Chowla and Selberg, Inventiones Math. J+5 (1978), 193–211.Google Scholar
7. Shimura, G. and Taniyama, Y., Complex multiplication of abelian verieties and its applications to number theory, Math. Soc. Japan, Tokyo, 1961.Google Scholar