Non-Archimedean and tropical theta functions


Journal Article

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. 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.

Full Text

Duke Authors

Cited Authors

  • Foster, T; Rabinoff, J; Shokrieh, F; Soto, A

Published Date

  • December 1, 2018

Published In

Volume / Issue

  • 372 / 3-4

Start / End Page

  • 891 - 914

International Standard Serial Number (ISSN)

  • 0025-5831

Digital Object Identifier (DOI)

  • 10.1007/s00208-018-1646-3

Citation Source

  • Scopus