Infinitely wildly ramified arboreal representations for postcritically finite polynomials with potential good reduction

2023/10/13 by Feiner, Alex
#11R32 #37P20 (Primary) 37P50 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.09372

Abstract

Let K be a number field, let v be a finite place of K, let f∈ K[z] be a degree d\geqslant2 polynomial with v|d, and let a∈ K. We show that if f is postcritically bounded and has potential good reduction with respect to v, then the arboreal representation associated to the pair (f,a) is either finite or infinitely wildly ramified above v.

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