Simple Factors in the Jacobian of a Fermat Curve

Abstract

Letdenote theNth Fermat curve. The period lattice ofF(N)is contained with finite index in the product of certain latticesLr,s(see [6]), and to this inclusion of lattices there corresponds an isogeny of the Jacobian ofF(N)onto a product of abelian varieties. The purpose of this paper is to determine when two factors in this product are isogenous overC, and whether they are absolutely simple.