I wonder about the notion of a spin structure for varieties over any field and results in this direction. For example, I wonder if there is something like a spin-bundle for the sphere $x^2+y^2+z^2=R^2$ and the projective space qith $q^2+q+1$ elements for the finite fields $\mathbb{F}_q$ depending on $q$

Thanx in advance! Simon

PS: I have read something in Spin structures on schemes, and it seems the question has to do with an existence of a nondegenerate quadratic form on the

I wonder about the notion of a spin structure for varieties over any field and results in this direction. For example, I wonder if there is something like a spin-bundle for the sphere $x^2+y^2+z^2=R^2$ and the projective space qith $q^2+q+1$ elements for the finite fields $\mathbb{F}_q$ depending on $q$

Thanx in advance! Simon

PS: I have read something in Spin structures on schemes, and it seems the question has to do with an existence of a nondegenerate quadratic form on the