2013/05/13 by Richard Pink, Pink, Richard · 2 citations
Computer Science · Mathematics · #14H10) #20E08 #37P05 (37P45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.AG #math.GR #msc:20E08 #msc:37P05 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1305.2841
Changes in version 3: various notation, numbering, arrangement, but mathematical content essentially the same
openalex publication_date 2013/05/13 · arxiv created 2013/08/26 · arxiv updated 2013/08/27 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We show that for any integer n and any field k of characteristic different from 2 there are at most finitely many isomorphism classes of quadratic morphisms from the projective line over k to itself with a finite postcritical orbit of size n. As a consequence we prove that every postcritically finite quadratic morphism over a field of positive characteristic can be lifted to characteristic zero with the same combinatorial type of postcritical orbit. The associated profinite geometric monodromy group is therefore the same as in characteristic zero, where it can be described explicitly by generators as a self-similar group acting on a regular rooted binary tree.