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Abstract. Information about the absolute Galois group G K of a number field K is encoded in how it acts on the ´etale fundamental group π of a curve X defined over K. In the case that K = Q ( ζ n ) is the cyclotomic field and X is the Fermat curve of degree n ≥ 3, Anderson determined the action of G K on the ´etale homology with coefficients in Z/nZ. The ´etale homology is the first quotient in the lower central series of the ´etale fundamental group. In this paper, we determine the Galois module structure of the graded Lie algebra for π. As a consequence, this determines the action of G K on all degrees of the associated graded quotient of the lower central series of the ´etale fundamental group of the Fermat curve of degree n, with coefficients in Z/nZ.
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Davis, Rachel; Pries, Rachel (, Journal of Algebra)null (Ed.)
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Lugo Charriez, Kathleen; Soledade Lemos, Leila; Carrazana, Yailee; Rodríguez-Casariego, Javier A.; Eirin-Lopez, Jose M.; Hauser-Davis, Rachel Ann; Gardinali, Piero; Quinete, Natalia (, Bulletin of Environmental Contamination and Toxicology)null (Ed.)
