Abstract
One of the fundamental constructions in Commutative and Local Algebra is the completion of a commutative Noetherian (unitary) ring A with respect to an ideal I of A (I ≠ A), see e.g. [116], or [133], or [121], or [7]. This allows one to associate to A another commutative Noetherian (unitary) ring  (which is called the I-adic completion of A) together with a flat homomorphism of unitary rings ϕ: A →  such that: i)  is a commutative Noetherian ring of Krull dimension = dim(A), which is complete with respect to the Î:= I Â-adic topology of Â, and ii) The canonical homomorphisms A/In → Â/În induced by ϕ are isomorphisms for every positive integer n ≥ 1. KeywordsCoherent SheaveCoherent SheafCanonical HomomorphismIrreducible VarietyClosed SubvarietyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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