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Results tagged with perfectoid-spaces
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user 91375
12
votes
1
answer
759
views
An explicit isomorphism $K^\times/K^{\times p} \cong K^\flat/\wp K^\flat$ where $K \supset \...
Let $K$ be a perfectoid field of mixed characteristic $(0, p)$, i.e. $K$ has characteristic $0$ but its residue field has characteristic $p$. Further suppose that $K$ contains all the $p$th roots of u …
- 435
2
votes
0
answers
160
views
flat resolutions of almost modules?
Recall the set-up in 2.4.10 of Almost Ring Theory by Ofer Gabber and Lorenzo Ramero:
$V$ is a commutative unital ring.
$\newcommand{\gm}{{\mathfrak m}}\gm$ is an ideal in $V$ such that $\gm^2 = \gm$. …
- 435
6
votes
1
answer
1k
views
Proposition 5.13 (ii) in Scholze's Perfectoid Spaces
In Proposition 5.13 (ii) in Scholze's Perfectoid Spaces, we have $R \to S$ a morphism of $\Bbb F_p$-algebras and the assumption that the relative Frobenius $\Phi_{S/R}$ induces an isomorphism $R_{(\Ph …
- 435