Abstract
We show that a coherent analytic sheaf \({\mathcal F}\) with prof \({{\mathcal F}\geq 2}\) defined outside a holomorphically convex compact set K in a 1-convex space X admits a coherent extension to the whole space X if, and only if, the canonical topology on \({H^1(X \setminus K,{\mathcal F})}\) is separated.
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Vâjâitu, V. An extension of coherent sheaves defined outside holomorphically convex compact sets. Annali di Matematica 191, 711–724 (2012). https://doi.org/10.1007/s10231-011-0202-5
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DOI: https://doi.org/10.1007/s10231-011-0202-5