Finite index theorems for iterated Galois groups of preperiodic points for unicritical polynomials

2025/08/01 by Minsik Han, Han, Minsik, Thomas J. Tucker +1
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Cryptography and Residue Arithmetic

paper · pdf · doi:10.48550/arxiv.2508.00266

Abstract

Let K be a number field and let f(x) = x^q + c where q is a prime power, c is in K, and f is not post-critically finite. We show that for any strictly preperiodic b in K, the iterated Galois group at b with respect to f has finite index in the generic iterated Galois group for f.

Citations

• ABC implies a Zsigmondy principle for ramification
• Finite ramification for preimage fields of postcritically finite morphisms

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