Hostname: page-component-848d4c4894-ttngx Total loading time: 0 Render date: 2024-05-24T09:15:09.545Z Has data issue: false hasContentIssue false
  • English
  • Français

The jacobian of a cyclic quotient of a fermat curve

Published online by Cambridge University Press:  22 January 2016

Chong Hai Lim
Chong Hai Lim*
Affiliation:
Department of Mathematics University of California, Berkeley CA 94720, U.S.A.
*
Department of Mathematics Faculty of Science, National University of Singapore Kent Ridge, Singapore 0511
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.

Fix a positive integer m. Let Fm denote the Fermat curve over Q of degree m, given by the projective equation

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 73 - 92
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[ 1 ] Aoki, N., Simple Factors of the Jacobian of a Fermat Curve and the Picard number of a Product of Fermat Curves, to appear in Amer. J. Math.Google Scholar
[ 2 ] Coleman, R., Torsion points on Abelian étale coverings of P1 = {0,1, ∞}, Trans. AMS, 311 (1989), 185–208.Google Scholar
[ 3 ] Coleman, R., Lecture notes on Cyclotomy, Tokyo University (1985).Google Scholar
[ 4 ] Coleman, R. and McCallum, W., Stable reduction of Fermat curves and Jacobi sum Hecke characters, J. Reine Angew. Math., 385 (1988), 41–101.Google Scholar
[ 5 ] Greenberg, R., On the Jacobian variety of some algebraic curves, Compositio Math., 42 (1981), 345–359.Google Scholar
[ 6 ] Gross, B. and Rohrlich, D., Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math., 44 (1978), 201–224.CrossRefGoogle Scholar
[ 7 ] Ihara, Y., Profinite braid groups, Galois representations and complex multiplications, Ann. Math., 123 (1986), 43–106.Google Scholar
[ 8 ] Koblitz, N. and Rohrlich, D., Simple Factors in the Jacobian of a Fermat curve, Canadian J. Math., 20 (1978), 1183–1205.Google Scholar
[ 9 ] Lim, C. H., Endomorphisms of Jacobian varieties of Fermat curves, to appear in Compositio Math.Google Scholar
[10] Prapavessi, D. T., On Jacobi sum Hecke Characters of Conductor a Power of 2. Ph.D. thesis, University of California, Berkeley (1988).Google Scholar
[11] Rohrlich, D., Appendix to “On the Periods of Abelian Integrals and a Formula of Chowla and Selberg” by B. Gross, Invent. Math., 45 (1978), 193–211.Google Scholar
[12] Schmidt, C. G., Der Definitions-Köper fur den Zerfall einer Abelschen Varietat mit Komplexer Multiplikation, Math. Ann., 254 (1980), 201–210.CrossRefGoogle Scholar
[13] Shimura, G. and Taniyama, Y., Complex multiplication of Abelian Varieties and its Applications to Number Theory, Tokyo, Math. Soc. Japan (1961).Google Scholar