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arXiv:math/0312359 [math.NT]AbstractReferencesReviewsResources

On the Arakelov theory of elliptic curves

Robin de Jong

Published 2003-12-18, updated 2004-09-06Version 2

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.

Comments: 17 pages. 2nd version; same main results as in v1, but with a section added on the average height of quotients of an elliptic curve
Journal: l'Ens. Math. 51 (2005), 179--201
Categories: math.NT, math.AG
Subjects: 11G05, 14G40, 14H52, 14K02
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