On ovoids of <i>O(5,q)</i>

Abstract

This article is about ovoids of the generalised quadrangle Oð5; qÞ and, equivalently, spreads of the generalised quadrangle Spð4; qÞ. In a less than conventional way the quadrangles are represented in the field GFðq 4 Þ which allows some amount of computation to be done. It is shown that an ovoid of Oð5; qÞ meets an elliptic quadric in 1 modulo p points.