Could you please give a reference or a sketch of a proof for the following proposition?
Proposition: The integral closure of a complete local Noetherian domain $R$ is module-finite over $R$
You can find the statement here, at pag. 4 (12).
2025-01-13 07:37:44.1736753864
Reference on a result about integral closures.
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You even have more:
Which means such a ring is a noetherian integral domain with the property that its integral closure in a finite extension of its field of fractions is module finite.
You'll find a proof in Bourbaki, Commutative Algebra Ch. IX, Complete local noetherian rings, § 4, no 2, theorem 2.