The classifying element for quotients of Fermat curves

Suppose C is a cyclic Galois cover of the projective line branched at the three points 0, 1, and ∞ . Under a mild condition on the ramification, we determine the structure of the graded Lie algebra of the lower central series of the fundamental group of C in terms of a basis which is well-suited to...

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Bibliographic Details
Published inCommunications in algebra Vol. 52; no. 10; pp. 4327 - 4341
Main Authors Duque-Rosero, Juanita, Pries, Rachel
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 02.10.2024
Taylor & Francis Ltd
Subjects
Absolute Galois group
Belyi curve
classifying element
covering
curve
Fermat curve
fundamental group
Galois module
graded Lie algebra
homology
Lie groups
lower central series
modular symbol
Primary: 11D41
Secondary: 11F06
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Summary:Suppose C is a cyclic Galois cover of the projective line branched at the three points 0, 1, and ∞ . Under a mild condition on the ramification, we determine the structure of the graded Lie algebra of the lower central series of the fundamental group of C in terms of a basis which is well-suited to studying the action of the absolute Galois group of Q .
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2346299