Galois action on homology of generalized Fermat Curves

2019/05/10 by Kontogeorgis, Aristides, Paramantzoglou, Panagiotis
#11G30 #14G32 #14H37 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.04298

Abstract

The fundamental group of Fermat and generalized Fermat curves is computed. These curves are Galois ramified covers of the projective line with abelian Galois groups H. We provide a unified study of the action of both cover Galois group H and the absolute Galois group Gal(\Q/\Q) on the pro-ℓ homology of the curves in study. Also the relation to the pro-ℓ Burau representation is investigated.

Related

• Galois action on the homology of Fermat curves
• Galois Action on Homology of the Heisenberg Curve
• The Galois action and cohomology of a relative homology group of Fermat\n Curves
• The Galois action on the lower central series of the fundamental group of the Fermat curve
• Monodromy of Fermat Surfaces and Modular Symbols for Fermat curves