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arXiv · 1610.02006

The Galois action and cohomology of a relative homology group of Fermat Curves

Rachel Davis·Rachel Pries·Vesna Stojanoska·Kirsten Wickelgren
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Abstract

For an odd prime $p$ satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group $G_{\mathbb{Q}(\zeta_p)}$ on the homology of the degree $p$ Fermat curve, building on work of Anderson. Further, we study the invariants and the first Galois cohomology group which are associated with obstructions to rational points on the Fermat curve.

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Rachel Davis, Rachel Pries, Vesna Stojanoska, Kirsten Wickelgren. 2016-10-06. The Galois action and cohomology of a relative homology group of Fermat Curves. https://arxiv.org/abs/1610.02006

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