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Faltings height and Néron–Tate height of a theta divisor
Part of
Robin de Jong, Farbod Shokrieh
Journal:

Compositio Mathematica / Volume 158 / Issue 1 / January 2022

Published online by Cambridge University Press:

24 January 2022, pp. 1-32

Print publication:

January 2022
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We prove a formula, which, given a principally polarized abelian variety $(A,\lambda )$ over the field of algebraic numbers, relates the stable Faltings height of $A$ with the Néron–Tate height of a symmetric theta divisor on $A$. Our formula completes earlier results due to Bost, Hindry, Autissier and Wagener. The local non-archimedean terms in our formula can be expressed as the tropical moments of the tropicalizations of $(A,\lambda )$.