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arXiv · 1905.04298

Galois action on homology of generalized Fermat Curves

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

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Aristides Kontogeorgis, Panagiotis Paramantzoglou. 2019-05-10. Galois action on homology of generalized Fermat Curves. https://arxiv.org/abs/1905.04298

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