On the intersection of ovoids sharing a polarity

In this article, an ovoidal fibration is used to show that any two ovoids of PG(3, q), q even, sharing a polarity, must meet in an odd number of points. This result was previously known only when one of the ovoids was an elliptic quadric or a Tits ovoid. It is also shown that an ovoid and an elliptic quadric of PG(3, q), sharing all of their tangents, must meet in 1 (mod 4) points.