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

General Mathematics

Access to Document

10.1007/s00013-021-01609-w

Cite this

@article{6aae28cbf14742b1bee4c4ace537507f,

title = "On Stoll{\textquoteright}s criterion for the maximality of quadratic arboreal Galois representations",

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.",

keywords = "Arboreal Galois representation, Automorphism group, Wreath product",

author = "Li, \{Hua Chieh\}",

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.",

year = "2021",

month = aug,

doi = "10.1007/s00013-021-01609-w",

language = "English",

volume = "117",

pages = "133--140",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Springer International Publishing",

number = "2",

}

TY - JOUR

T1 - On Stoll’s criterion for the maximality of quadratic arboreal Galois representations

AU - Li, Hua Chieh

PY - 2021/8

Y1 - 2021/8

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85104498168

UR - https://www.scopus.com/pages/publications/85104498168#tab=citedBy

U2 - 10.1007/s00013-021-01609-w

DO - 10.1007/s00013-021-01609-w

M3 - Article

AN - SCOPUS:85104498168

SN - 0003-889X

VL - 117

SP - 133

EP - 140

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this