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.
Citation
Hideaki Ikoma. "The Faltings-Moriwaki modular height and isogenies of elliptic curves." J. Math. Kyoto Univ. 48 (3) 661 - 682, 2008. https://doi.org/10.1215/kjm/1250271389
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