Collineations Of Polar Spaces

Abstract

In this paper we consider general embeddable polar spaces with Witt index at least three. If π : S( ξ) —> S( ξ’) be a thick collineation between polar spaces with i( ξ) =i( ξ’) ≥3. Then there exists a place Ø: k—> k' U ∞ with valuation ring A = Ø^-1 (K'), an A- module M in V with Mk = V and a Ø-scmilinear mapping β: M —> V’ such that π (X) = β (M∩X) K' for all points X in S (ξ).