On the Arakelov theory of elliptic curves

Details On the Arakelov theory of elliptic curves On the Arakelov theory of elliptic curves

2003-12-18

arxiv.org/abs/math/0312359v2

l'Ens. Math. 51 (2005), 179--201

Mathematics

Number Theory

17 pages. 2nd version; same main results as in v1, but with a section added on the average height of quotients of an elliptic

Scientific paper

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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