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

Abstract

For an odd prime $p$ satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group $G_{\mathbb{Q}(\hat{I}{\P }_p)}$ 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.

Minor improvements based on referee report