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Results tagged with perfectoid-spaces
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user 6074
9
votes
Accepted
An explicit isomorphism $K^\times/K^{\times p} \cong K^\flat/\wp K^\flat$ where $K \supset \...
Here is an explicit description of the isomorphism: It takes $a\in K^\flat$ to the class of $1+(\zeta_p-1)^p a^{1/p^n}\in K^\times$ for any large enough $n$ (the image modulo $p$-th powers is independ …
- 21.3k
16
votes
Accepted
How many untilts?
This specific question is probably not addressed in the literature; let's try to figure it out!
Let $K$ be an algebraic extension of $\mathbb Q_p$ such that the tilt of $\widehat{K}$ is isomorphic to …
- 21.3k
11
votes
Perfectoid approach to resolution of singularities in char $p$
Somehow that question slipped my radar, sorry!
The truth is that shamefully I'm not able to say much, as I don't have a strong knowledge of resolution of singularities. But at least so far, the flow o …
- 21.3k
9
votes
Accepted
Proposition 5.13 (ii) in Scholze's Perfectoid Spaces
Regarding the first and third question, what you say is correct. For the second question, you are looking for the base change compatibility of the cotangent complex: If $R\to R'$ is any map of rings a …
- 21.3k
9
votes
Some questions from the paper by Scholze-Weinstein
In Lemma 4.1.7, we actually assume that $R$ is f-semiperfect (i.e. a quotient of a perfect ring by a finitely generated ideal); I doubt the result is true without this assumption.
Note that $W_{PD}$ i …
- 21.3k
13
votes
Accepted
On the definition of the etale site of an adic space
Great question!
The short answer is that Huber simply wanted to be in a setting where everything is (stably) sheafy, and so put some assumptions ensuring this. Note that Huber's work remained somewhat …
- 21.3k