Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering Valuations on Demushkin Fields   Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}_2}(2)$, where $G_F(2)$
denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$.
We prove that then $K$ admits a (non-trivial) valuation $v$ which is
2-henselian and has residue field $\mathbb{F}_2$. Furthermore, $v(2)$ is a
minimal positive element in the value group $\Gamma_v$ and
$[\Gamma_v:2\Gamma_v]=2$. This forms the first positive result on a more
general conjecture about the structure of pro-$p$ Galois groups which we
formulate precisely (cf. Conjecture 1). As an application, we prove a strong
version of the birational section conjecture for smooth, complete curves $X$
over $\mathbb{Q}_2$, as well as an analogue for varieties.

1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an