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Non-Archimedean and tropical theta functions | | Tyler Foster
; Joseph Rabinoff
; Farbod Shokrieh
; Alejandro Soto
; | | Date: |
23 May 2017 | | 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. | | Source: | arXiv, 1705.8212 | | Services: | Forum | Review | PDF | Favorites | |
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