Artin-Schreier geproci configurations in projective spaces of arbitrary dimension

Abstract: We construct finite geproci sets in every projective dimension and in every positive characteristic by introducing $\mathbb{F}_N$-Artin-Schreier configurations. In $\mathbb{P}<sup>3$, we characterize exactly when such configurations are geproci: an $\mathbb{F}_N$-Artin-Schreier configuration on $q$ lines spanning $\mathbb{P}<sup>3$ is $(q,N)$-geproci if and only if $q\leq N$. We then develop a lifting construction which produces geproci sets in $\mathbb{P}<sup>n$ for every $n\geq 3$.