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arXiv · 1810.02637

Faltings height and N\'eron-Tate height of a theta divisor

Robin de Jong·Farbod Shokrieh
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Abstract

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 N\'eron--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 $(A,\lambda)$.

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Robin de Jong, Farbod Shokrieh. 2018-10-05. Faltings height and N\'eron-Tate height of a theta divisor. https://doi.org/10.1112/s0010437x21007661

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