Group of Automorphisms of the Fermat Curve

Abstract

AbstractIn his paper ("Oevres Scientifiques, Collected Papers, Vol. III, pp. 329-342, Springer-Verlag, Berlin/New York, 1979), Well asserted (without proof) that the automorphism group of the Fermat hypersurface of exponent N and dimension r − 1 over an algebraically closed field of characteristic prime to N is the semidirect product of the symmetric group on r + 1 letters and the direct sum of r copies of the cyclic group of order N. It turns out that the assertion is false in positive characteristic. In this paper, we present a proof of Weil′s assertion for the case of the Fermat curves (r = 2) in characteristic 0