Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Odoni's conjecture on arboreal Galois representations is false   Suppose $f \in K[x]$ is a polynomial. The absolute Galois group of $K$ acts
on the preimage tree $\mathrm{T}$ of $0$ under $f$. The resulting homomorphism
$\phi_f: \mathrm{Gal}_K \to \mathrm{Aut} \mathrm{T}$ is called the arboreal
Galois representation. Odoni conjectured that for all Hilbertian fields $K$
there exists a polynomial $f$ for which $\phi_f$ is surjective. We show that
this conjecture is false.

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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an