论文标题
奥多尼对树木纪念碑的猜想是错误的
Odoni's conjecture on arboreal Galois representations is false
论文作者
论文摘要
假设K [x] $中的$ f \是多项式。 $ k $的绝对Galois集团在$ f $下的PreImage Tree $ \ Mathrm {T} $ $ 0 $上表现出来。结果同构$ ϕ_f：\ mathrm {gal} _k \ to \ mathrm {aut} \ mathrm {t} $称为Arboreal Galois表示。奥多尼（Odoni）猜想，对于所有希尔伯特（Hilbertian）字段$ k $，都有一个多项式$ f $，其中$ ϕ_f $是溢流的。我们证明了这个猜想是错误的。
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 $ϕ_f: \mathrm{Gal}_K \to \mathrm{Aut} \mathrm{T}$ is called the arboreal Galois representation. Odoni conjectured that for all Hilbertian fields $K$ there exists a polynomial $f$ for which $ϕ_f$ is surjective. We show that this conjecture is false.
