Let $A$ be an integral domain with the $I$-adic filtration. Let $B$ be the fraction field of $A$. My question is the following:
Is the fraction field of the completion of $A$ the same as the completion of $B$?
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zcn
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2What does fraction field completion of $K$ mean? – Seth Apr 11 '14 at 00:14
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I interpreted your question as being whether or not taking fraction fields commutes with $I$-adic completion. Please edit if your question is in fact something different (note also that the question does not make sense unless $\widehat{A}^I$ is a domain, i.e. $I$ is analytically irreducible) – zcn Apr 11 '14 at 04:50
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Related http://math.stackexchange.com/questions/38152/do-localization-and-completion-commute and http://mathoverflow.net/questions/64399/does-completion-commute-with-localization – Ehsan M. Kermani Apr 11 '14 at 05:00