Schmidt rank of quartics over perfect fields

Abstract

Let $k$ be a perfect field of characteristic $\ne 2$. We prove that the Schmidt rank (also known as strength) of a quartic polynomial $f$ over $k$ is bounded above in terms of only the Schmidt rank of $f$ over $\overline{k}$, an algebraic closure of $k$.

13 pages. arXiv admin note: text overlap with arXiv:2107.08080