Galois action on homology of generalized Fermat Curves

Kontogeorgis, Aristides and Paramantzoglou, Panagiotis

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 \\$\\mathrm\\{Gal\\}(\\bar\\{\\mathbb\\{Q\\}\\}/\\mathbb\\{Q\\})\\$ on the pro-\\$\\ell\\$ homology of the curves in study. Also the relation to the pro-\\$\\ell\\$ Burau representation is investigated.}