Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Galois groups of large fields with simple theory (with an appendix by
  Philip Dittmann)   Suppose that $K$ is an infinite field which is large (in the sense of Pop)
and whose first order theory is simple. We show that $K$ is {\em bounded},
namely has only finitely many separable extensions of any given finite degree.
We also show that any genus $0$ curve over $K$ has a $K$-point and if $K$ is
additionally perfect then $K$ has trivial Brauer group. These results give
evidence towards the conjecture that large simple fields are bounded PAC.
Combining our results with a theorem of Lubotzky and van den Dries we show that
there is a bounded $\mathrm{PAC}$ field $L$ with the same absolute Galois group
as $K$. In the appendix we show that if $K$ is large and $\mathrm{NSOP}_\infty$
and $v$ is a non-trivial valuation on $K$ then $(K,v)$ has separably closed
Henselization, so in particular the residue field of $(K,v)$ is algebraically
closed and the value group is divisible. The appendix also shows that formally
real and formally $p$-adic fields are $\mathrm{SOP}_\infty$ (without assuming
largeness).

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The categories of this paper are: cs
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The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
20
The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: physics