External points to a conic from a Baer subplane

Abstract

For an irreducible conic $\mathcal{C}$ in a Desarguesian plane of odd square order, estimating the number of points from a Baer subplane which are external to $\mathcal{C}$ is a natural problem. In this paper, a complete list of possibilities is determined for the case where $\mathcal{C}$ shares at least one point with the subplane.