A characterization of point-line geometries for finite buildings (Q1107818)

It has always been an attractive task to characterize interesting geometries (of higher rank) as incidence systems (point/line geometries) with some natural axioms. The oldes such result is probably the characterization of projective space by Veblen and Young. The author characterizes the point/line geometries of almost all finite buildings as pseudopolar spaces satisfying a certain axiom (R). This theorem extends (and uses) the already classical work by Tits, Veldkamp, Buekenhout, Shult, Cooperstein and Cohen as well as more recent results by the author. In fact, only the idea of the proof, which is an induction on the rank, is given.