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^*

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

摘要

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.

原文	英語
頁（從 - 到）	133-140
頁數	8
期刊	Archiv der Mathematik
卷	117
發行號	2
DOIs	https://doi.org/10.1007/s00013-021-01609-w
出版狀態	已發佈 - 2021 8月

ASJC Scopus subject areas

一般數學

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10.1007/s00013-021-01609-w

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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.",

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

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

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

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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

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