Questions tagged [formal-schemes]

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Global version of Gabber's rigidity theorem

I had a question regarding Gabber's rigidity. Let $A$ be a ring (let's assume Noetherian) and $I$ be an ideal, since the pair $(\hat{A},I)$ is a henselian pair ($\hat{A}$ is the completion along $I$), ...
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5 votes
1 answer
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Are formal completions along a subvariety only dependent on the normal bundle?

In his paper "Mukai flops and derived categories", Namikawa reduces a general Mukai flop of a smooth projective $2n$-dimensional variety $Z$ along a subvariety $W\cong \mathbb P^n$ with $N_{W/Z}\cong \...
HNuer's user avatar
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1 vote
0 answers
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Does analytic isomorphism imply local isomorphism?

If $ \mathfrak{p} $ is a (not necessarily closed) point of a variety $ \operatorname{Spec}(A) $, and $ \mathfrak{q} $ is a (not necessarily closed) point of a variety $ \operatorname{Spec}(B) $ such ...
Schemer1's user avatar
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18 votes
3 answers
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Non-algebraizable Formal Scheme?

What is an example of a formal scheme that is not algebraizable? Recall that, if $X$ is a locally noetherian scheme and $Z$ is a closed subset (of the underlying topological space), then one can form ...
5 votes
0 answers
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Colimit of nilpotent thickenings in the category of schemes

This question is highly related to this and this one. Given a ring $A$ and an ideal $I$, the direct system of schemes $\text{Spec}(A/I)\rightarrow \text{Spec}(A/I^2)\rightarrow \ldots$ has a colimit ...
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2 votes
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Does there exists a "local slice" for an action $ \widehat{\mathbb{G}_{a}} $ on $ \operatorname{Spf}(\widehat{A}) $ (char zero)?

Every action $ \beta $ of $ \mathbb{G}_{a} $ on a variety $ \operatorname{Spec}(A) $ over a field of characteristic zero is obtained from a locally nilpotent derivation $ \delta $ via $ f(t_{0} \ast x)...
Schemer1's user avatar
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