Continuous closure of sheaves
Commutative Algebra
2010-10-27 v1 Algebraic Geometry
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.
Cite
@article{arxiv.1010.5480,
title = {Continuous closure of sheaves},
author = {János Kollár},
journal= {arXiv preprint arXiv:1010.5480},
year = {2010}
}