• Corpus ID: 119131663

# The motivic anabelian geometry of local heights on abelian varieties

@article{Betts2017TheMA,
title={The motivic anabelian geometry of local heights on abelian varieties},
author={L. Alexander Betts},
journal={arXiv: Number Theory},
year={2017}
}
• L. A. Betts
• Published 15 June 2017
• Mathematics
• arXiv: Number Theory
We study the problem of describing local components of height functions on abelian varieties over characteristic $0$ local fields as functions on spaces of torsors under various realisations of a $2$-step unipotent motivic fundamental group naturally associated to the defining line bundle. To this end, we present three main theorems giving such a description in terms of the $\mathbb Q_\ell$- and $\mathbb Q_p$-pro-unipotent etale realisations when the base field is $p$-adic, and in terms of the…
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