Non-Archimedean and tropical theta functions
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--L\"utkebohmert theory of non-Archimedean theta functions for abelian varieties with semi-abelian reduction.
Cite
@article{arxiv.1705.08212,
title = {Non-Archimedean and tropical theta functions},
author = {Tyler Foster and Joseph Rabinoff and Farbod Shokrieh and Alejandro Soto},
journal= {arXiv preprint arXiv:1705.08212},
year = {2018}
}
Comments
Final version to appear in Mathematische Annalen. Full-text view-only journal version is available at http://rdcu.be/E5tM . Note the journal version has a slightly different numbering system