On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

Hua Chieh Li

doi:10.1007/s00013-021-01609-w

On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

Hua Chieh Li^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that for a quadratic polynomial f(x) = x²- c, where c= (8 k+ 2) (8 k+ 3) or c= (4 k+ 1) (4 k+ 2) + 1 with k∈ N∪ { 0 } , the Galois group of the splitting field of each iterate fⁿ of f is isomorphic to the automorphism group of a complete binary rooted tree of height n.

Original language	English
Pages (from-to)	133-140
Number of pages	8
Journal	Archiv der Mathematik
Volume	117
Issue number	2
DOIs	https://doi.org/10.1007/s00013-021-01609-w
Publication status	Published - 2021 Aug

Keywords

Arboreal Galois representation
Automorphism group
Wreath product

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00013-021-01609-w

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abstract = "We show that for a quadratic polynomial f(x) = x2- c, where c= (8 k+ 2) (8 k+ 3) or c= (4 k+ 1) (4 k+ 2) + 1 with k∈ N∪ { 0 } , the Galois group of the splitting field of each iterate fn of f is isomorphic to the automorphism group of a complete binary rooted tree of height n.",

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author = "Li, {Hua Chieh}",

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AB - We show that for a quadratic polynomial f(x) = x2- c, where c= (8 k+ 2) (8 k+ 3) or c= (4 k+ 1) (4 k+ 2) + 1 with k∈ N∪ { 0 } , the Galois group of the splitting field of each iterate fn of f is isomorphic to the automorphism group of a complete binary rooted tree of height n.

KW - Arboreal Galois representation

KW - Automorphism group

KW - Wreath product

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On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

Abstract

Keywords

ASJC Scopus subject areas

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