On the separability of cyclotomic schemes over finite field

Abstract

It is proved that with finitely many possible exceptions, each cyclotomic scheme over finite field is determined up to isomorphism by the tensor of 2-dimensional intersection numbers; for infinitely many schemes, this result cannot be improved. As a consequence, the Weisfeiler-Leman dimension of a Paley graph or tournament is at most 3 with possible exception of several small graphs.