Journal of Mathematics of Kyoto University

The Faltings-Moriwaki modular height and isogenies of elliptic curves

Hideaki Ikoma

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Abstract

We estimate the variation of the Faltings-Moriwaki modular height under isogenies of elliptic curves. In particular, we reprove the Faltings finiteness theorem for elliptic curves over fields of finite type over $\mathbb{Q}$. Our approach is \lq\lqeffective\rq\rq in the sence that we generalize Raynaud's upper bound to higher dimensional cases.

Article information

Source
J. Math. Kyoto Univ., Volume 48, Number 3 (2008), 661-682.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250271389

Digital Object Identifier
doi:10.1215/kjm/1250271389

Mathematical Reviews number (MathSciNet)
MR2511056

Zentralblatt MATH identifier
1260.11047

Citation

Ikoma, Hideaki. The Faltings-Moriwaki modular height and isogenies of elliptic curves. J. Math. Kyoto Univ. 48 (2008), no. 3, 661--682. doi:10.1215/kjm/1250271389. https://projecteuclid.org/euclid.kjm/1250271389


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