Questions tagged [completion]

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17 votes
4 answers
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Completion of a local ring of a curve

Let $X$ be a smooth projective irreducible curve defined over an algebraically closed field $\mathbb{K}$ (of arbitrary characteristic), and let $p\in X$ be a closed point. Denote by $\mathcal{O}_p(X)$ ...
Jérémy Blanc's user avatar
6 votes
2 answers
1k views

Derived Nakayama for complete modules

I have encountered the following "Nakayama Lemma" recently: Let $A$ be a ring and $I$ some finitely generated ideal. Let $\mathcal C_\bullet$ be a chain complex of $I$-(derived) complete $A$-...
slinshady's user avatar
  • 309
6 votes
2 answers
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Why is $K_{\upsilon}|K$ separable for a global field $K$?

I asked this question on math.stackexchange but maybe it fits here better. If not, I apologize in advance and will remove the question. Let $K$ be a global field and $\upsilon$ a prime of $K$. Then ...
Frida's user avatar
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11 votes
4 answers
1k views

What kind of completion is this?

Let $X$ be a compact Hausdorff space, and $C(X)$ the unital commutative C*-algebra of continuous functions on it. The double Banach dual $C(X)^{**}$ is a commutative von Neumann algebra and hence has ...
Chris Heunen's user avatar
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10 votes
1 answer
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Does completion commute with localization?

Suppose $A$ is a Noetherian (not necessarily local) ring and $\mathfrak{m}\subset A$ a maximal ideal. Then is it true that $$\hat{A}_{\hat{\mathfrak{m}}}=\widehat{A _{\mathfrak{m}}},$$ where hats ...
ashpool's user avatar
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7 votes
1 answer
595 views

Does Grothendieck's algebraization imply existence of colimits of schemes?

I am a little bit confused about two lemmas regarding Grothendieck's algebraization. Assume all algebras are defined over some field. Here is the short version of my question: Does Tag 09ZT ("...
user127776's user avatar
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