The classifying element for quotients of Fermat curves

2023/12/12 by Duque-Rosero, Juanita, Pries, Rachel
#11D41 #11F67 #11G30 #11G32 #13A50 #14F20 (secondary) #14F35 #14H30 #17B70 (primary) 11F06 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.07710

Abstract

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.

Related

• The Galois action on the lower central series of the fundamental group of the Fermat curve
• Galois action on the homology of Fermat curves
• Galois action on homology of generalized Fermat Curves
• Galois actions on fundamental groups of curves and the cycle C-C^-
• On cyclic groups covers of the projective line