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Results tagged with completion
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user 21278
11
votes
Accepted
Does Grothendieck's algebraization imply existence of colimits of schemes?
Here's one way to see what's going on. I will use the Tannakian duality theorem of Hall and Rydh (see Theorem 1.1 here). It is stated for algebraic stacks, but if you replace the word "algebraic stack …
- 2,607
17
votes
Completion of a local ring of a curve
Since $x$ and $y$ are non-zero in $\mathcal{O}_{X,p}$, they are non-zero in the completion since $\mathcal{O}_{X,p} \to \widehat{\mathcal{O}}_{X,p}$ is injective by Krull's Intersection Theorem. …
- 2,607