Modular symbols for Fermat curves
Modular symbols for Fermat curves
Let $F_n$ denote the Fermat curve given by $x^n+y^n=z^n$ and let $\mu _n$ denote the Galois module of $n$th roots of unity. It is known that the integral homology group $H_1(F_n,\mathbb {Z})$ is a cyclic $\mathbb {Z}[\mu _n\times \mu _n]$ module. In this paper, we prove this result using modular …