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arXiv · 1010.5480

Continuous closure of sheaves

János Kollár
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Abstract

We give a purely algebraic construction of the continuous closure of any finitely generated torsion free module; a concept first studied by H.~Brenner and M.~Hochster. The construction implies that, at least in characteristic 0, taking continuous closure commutes with flat morphisms whose fibers are semi-normal. This implies that the continuous closure of a coherent ideal sheaf is again a coherent ideal sheaf (both in the Zariski and in the \'etale topologies) and it commutes with field extensions.

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János Kollár. 2010-10-26. Continuous closure of sheaves. https://arxiv.org/abs/1010.5480

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