The Difference Kapranov Theorem
Algebraic Geometry
2025-02-12 v1 Logic
Abstract
This paper creates a link between \textit{Tropical Geometry} and \textit{Difference Algebra}. The main result is a difference version of \textit{Kapranov's Theorem}. In this theorem, we extend Kapranov's Theorem to the case of a Laurent difference polynomial with coefficients from a multiplicative valued difference field, where the residue field is an algebraically closed field with a generic automorphism (ACFA). A result of this paper that plays a critical role in the proof of the Difference Kapranov Theorem is a difference version of \textit{Newton's Lemma}.
Cite
@article{arxiv.2502.07607,
title = {The Difference Kapranov Theorem},
author = {Saba Aliyari},
journal= {arXiv preprint arXiv:2502.07607},
year = {2025}
}
Comments
41 pages, Derived from the author's PhD thesis