Geodesic
A characterisation of the generalized quadrangle $Q(5,q)$ using cohomology
Journal of Algebraic Combinatorics, Tome 15 (2002) no. 2, pp. 107-125.

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Summary: If a GQ $S O _{ x}$ O_x of $S Q$ Q (4,q),q even, and $O _{ x}$ O_x is an elliptic quadric for each $X Q$ Q (5,q). In this paper we provide a single proof for the $q$ odd and $q$ even cases by establishing a link between the geometry involved and the first cohomology group of a related simplicial complex.
Keywords: generalized quadrangle, subquadrangle, cohomology, ovoid 
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     author = {Brown, Matthew R.},
     title = {A characterisation of the generalized quadrangle $Q(5,q)$ using cohomology},
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     pages = {107--125},
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Brown, Matthew R. A characterisation of the generalized quadrangle $Q(5,q)$ using cohomology. Journal of Algebraic Combinatorics, Tome 15 (2002) no. 2, pp. 107-125. http://geodesic.mathdoc.fr/item/JAC_2002__15_2_a3/