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A note on tensor products of polar spaces over finite fields. (English) Zbl 0836.51004
The author’s abstract: “A symplectic or orthogonal space admitting a hyperbolic basis over a finite field is tensored with its Galois conjugates to obtain a symplectic or orthogonal space over a smaller field. A mapping between these spaces is defined which takes absolute points to absolute points. It is shown that caps go to caps. Combined with a result of Dye’s one obtains a simple proof of a result due to Blokhuis and Moorehouse that ovoids do not exist on hyperbolic quadrics in dimension ten over a field of characteristic two”.

##### MSC:
 51A50 Polar geometry, symplectic spaces, orthogonal spaces
##### Keywords:
polar space; caps; ovoids; hyperbolic quadrics
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