Dynamical Galois groups of trinomials and Odoni's conjecture

Abstract

We prove Odoni's conjecture in all prime degrees; namely, we prove that for every positive prime $p$, there exists a degree $p$ polynomial $\phi \in \mathbb{Z}[x]$ with surjective arboreal Galois representation. We also show that Vojta's conjecture implies the existence of such a polynomial in many degrees $d$ which are not prime.

References in corpus (1)

• Large arboreal Galois representations

Cited by in corpus (3)

• Large arboreal Galois representations
• The arithmetic basilica: a quadratic PCF arboreal Galois group
• Abelian extensions in dynamical Galois theory