A base change framework for tensor functions
Commutative Algebra
2026-03-11 v2 Computational Complexity
Combinatorics
Abstract
The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)} slice rank is linearly bounded by geometric rank for any 3-tensors over any field. \emph{(2)} slice rank of any 3-tensors is quasi-supermultiplicative. As a consequence, the asymptotic slice rank exists for any 3-tensors.
Cite
@article{arxiv.2603.07173,
title = {A base change framework for tensor functions},
author = {Qiyuan Chen},
journal= {arXiv preprint arXiv:2603.07173},
year = {2026}
}
Comments
There is some gap in the proof of Lemma4.3