A base change framework for tensor functions

Qiyuan Chen

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arXiv · 2603.07173

A base change framework for tensor functions

Qiyuan Chen

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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.

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Qiyuan Chen. 2026-03-07. A base change framework for tensor functions. https://arxiv.org/abs/2603.07173

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