Publications [#345764] of Joseph D Rabinoff

Papers Published

1. Foster, T; Rabinoff, J; Shokrieh, F; Soto, A, Non-Archimedean and tropical theta functions, Mathematische Annalen, vol. 372 no. 3-4 (December, 2018), pp. 891-914 [doi]
   (last updated on 2024/08/15)

   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.