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- Title
Galois action on homology of generalized Fermat Curves.
- Authors
Kontogeorgis, Aristides; 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.
- Subjects
ABELIAN groups; CURVES; FUNDAMENTAL groups (Mathematics)
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 4, p1377
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haaa038