Geodesic
Collineations of Polar Spaces
Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 296-309

Voir la notice de l'article provenant de la source Cambridge University Press

The fundamental theorem of projective geometry describes the bijective collineations between two projective spaces P V and P V′ of finite dimension (greater than one) over division rings k and k′ in terms of an isomorphism φ:k → k′ and a φ-semilinear bijective mapping between the underlying vector spaces V and V′. Tits [9, Theorem 8.611] has given an extensive generalization of this theorem to embeddable polar spaces induced by polarities coming from either (σ, )-hermitian forms or from (σ, )-quadratic forms with Witt indices at least two. In another direction, Klingenberg [7] and later André [1] and Rado [8], have generalized the fundamental theorem by considering non-injective collineations. Now the isomorphism φ must be replaced by a place φ:k → k′ ∪ ∞ and an integral structure over the valuation ring A = φminus1(k′) is induced into the projective space P V. 
James, Donald G. Collineations of Polar Spaces. Canadian journal of mathematics, Tome 37 (1985) no. 2, pp. 296-309. doi: 10.4153/CJM-1985-018-6
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