Galois action on homology of generalized Fermat Curves
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 . We provide a unified study of the action of both cover Galois group and the absolute Galois group $\mathrm{Gal}(\bar{\Q}/\Q)$ on the pro- homology of the curves in study. Also the relation to the pro- Burau representation is investigated.
35 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1804.07021