A note on the Bilinear Bogolyubov Theorem: Transverse and bilinear sets

Pierre-Yves Bienvenu, Diego González-Sánchez, Ángel D. Martínez

A set $P\subset {\mathbb{F}}_p^n\times {\mathbb{F}}_p^n$ is called $\text{bilinear}$ when it is the zero set of a family of linear and bilinear forms, and $\text{transverse}$ when i…