On Freiman's Theorem in a function field setting

Mieke Wessel

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arXiv · 2405.10724

On Freiman's Theorem in a function field setting

Mieke Wessel

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Abstract

We prove some new instances of a conjecture of Bachoc, Couvreur and Z\'emor that generalizes Freiman's $3k-4$ Theorem to a multiplicative version in a function field setting. As a consequence we find that if $F$ is a rational function field over an algebraically closed field $K$ and $S \subset F$ a finite dimensional $K$-vector space such that $\dim S^2 = 2\dim S + 1$, then the conjecture holds.

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Mieke Wessel. 2024-05-17. On Freiman's Theorem in a function field setting. https://arxiv.org/abs/2405.10724

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