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Mordell-Weil groups of the Jacobian of the 5-th Fermat curve

Authors:	Pavlos Tzermias

Institution:	Department of Mathematics, University of California, Berkeley, California 94720

Abstract:	Let $J_{5}$ denote the Jacobian of the Fermat curve of exponent 5 and let $K=Q(\zeta _{5})$ . We compute the groups $J_{5}(K)$ , $J_{5}(K^{+})$ , $J_{5}(Q)$ , where $K^{+}$ is the unique quadratic subfield of . As an application, we present a new proof that there are no -rational points on the 5-th Fermat curve, except the so called ``points at infinity".

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