Abstract
In this paper I consider the question of when formal vector bundles on the formal scheme obtained by completing the punctured spectrum of a ring of formal power series along a closed subscheme are algebraic. This leads to a generalization of Zariski's theorem about purity of branch loci to rings whose embedding dimension is not much bigger than their Krull dimension. By applying it to the local ring in the vertex of the affine cone over some projective space we see that for an irreducible scheme X _ Pk, where k is an algebraically closed field, the algebraic fundamental group vanishes, if dim(X) > n/2. This result was also obtained by Fulton and Hansen (see [FHI), and special cases were obtained previously by Barth (where k = C, and X is
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