Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decompletion of cyclotomic perfectoid fields in positive characteristic   Let $E$ be a field of characteristic $p$. The group $\mathbf{Z}_p^\times$
acts on $E((X))$ by $a \cdot f(X) = f((1+X)^a-1)$. This action extends to the
$X$-adic completion $\tilde{\mathbf{E}}$ of $\cup_{n \geq 0} E((X^{1/p^n}))$.
We show how to recover $E((X))$ from the valued field $\tilde{\mathbf{E}}$
endowed with its action of $\mathbf{Z}_p^\times$. To do this, we introduce the
notion of super-H\"older vector in certain $E$-linear representations of
$\mathbf{Z}_p$. This is a characteristic $p$ analogue of the notion of locally
analytic vector in $p$-adic Banach representations of $p$-adic Lie groups.

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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol