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We prove the classification of the real vector subspaces of a quaternionic vector space by using a covariant functor which associates, to any pair formed of a quaternionic vector space and a real subspace, a coherent sheaf over the sphere.

CoGalois groups appear in a natural way in the study of covers. They generalize the well-known group of covering automorphisms associated with universal covering spaces. Recently, it has been proved that each quasi-coherent sheaf over the projective line $\bm{P}^1(R)$ ($R$ is a commutative ring) admits a flat cover and so we have the associated coGalois group of the cover. In general the problem of computing coGalois groups is difficult. We study a wide class of quasi-coherent sheaves whose associated coGalois groups admit a very accurate description in terms of topological properties. This class includes finitely generated and cogenerated sheaves and therefore, in particular, vector bundles.

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SYNTHETIC LIE THEORY

On the classification of the real vector subspaces of a quaternionic vector space

THE GROUP OF COVERING AUTOMORPHISMS OF A QUASI-COHERENT SHEAF ON $\bm{P}^1(K)$

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3 results

SYNTHETIC LIE THEORY

On the classification of the real vector subspaces of a quaternionic vector space

THE GROUP OF COVERING AUTOMORPHISMS OF A QUASI-COHERENT SHEAF ON $\bm{P}^1(K)$