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arXiv · 1705.08212

Non-Archimedean and tropical theta functions

Tyler Foster·Joseph Rabinoff·Farbod Shokrieh·Alejandro Soto
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Abstract

We define a tropicalization procedure for theta functions on abelian varieties over a non-Archimedean field. We show that the tropicalization of a non-Archimedean theta function is a tropical theta function, and that the tropicalization of a non-Archimedean Riemann theta function is a tropical Riemann theta function, up to scaling and an additive constant. We apply these results to the construction of rational functions with prescribed behavior on the skeleton of a principally polarized abelian variety. We work with the Raynaud--Bosch--Lütkebohmert theory of non-Archimedean theta functions for abelian varieties with semi-abelian reduction.

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Tyler Foster, Joseph Rabinoff, Farbod Shokrieh, Alejandro Soto. 2018-01-19. Non-Archimedean and tropical theta functions. https://doi.org/10.1007/s00208-018-1646-3

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