The Galois action and cohomology of a relative homology group of Fermat   Curves
  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. 
Rachel Davis, Rachel Pries, Vesna Stojanoska, and Kirsten Wickelgren
math.NT math.AG math.AT