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On the Arakelov theory of elliptic curves

Robin de Jong
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Abstract

This note contains an elementary discussion of the Arakelov intersection theory of elliptic curves. The main new results are a projection formula for elliptic arithmetic surfaces and a formula for the "energy" of an isogeny between Riemann surfaces of genus 1. The latter formula provides an answer to a question originally posed by Szpiro.

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Robin de Jong. 2003-12-18. On the Arakelov theory of elliptic curves. https://arxiv.org/abs/math/0312359

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