Let $R$ be a regular local complete (with respect to the maximal ideal) ring with field of fraction $K$. Let $S$ be a Noetherian local ring which is an $R$-algebra. Is the completed tensor product (https://stacks.math.columbia.edu/tag/0AMU) $S \widehat{\otimes}_R K$ a Noetherian local ring containing $K$ ?
On Noetherianity and local ness of a completed tensor product
Snake Eyes
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