Math @ Duke

Publications [#345764] of Joseph D Rabinoff
Papers Published
 Foster, T; Rabinoff, J; Shokrieh, F; Soto, A, NonArchimedean and tropical theta functions,
Mathematische Annalen, vol. 372 no. 34
(December, 2018),
pp. 891914 [doi]
(last updated on 2021/05/15)
Abstract: We define a tropicalization procedure for theta functions on abelian varieties over a nonArchimedean field. We show that the tropicalization of a nonArchimedean theta function is a tropical theta function, and that the tropicalization of a nonArchimedean 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 nonArchimedean theta functions for abelian varieties with semiabelian reduction.


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