Über die Automorphismengruppe des Fermatkörpers Original Research Article

In this paper the full group of automorphisms of the curvexn+yn=znover an algebraically closed field of arbitrary characteristicpgreater-or-equal, slanted0 is determined. It turns out that in general the group is of order 6n2and of the structure known from characteristic 0. However there are exceptional cases, namely characteristicp>0 and exponentn=1+ph>3. In this case the automorphism group is the projective unitary groupPGU(3, q) (withq=ph) of order (q3+1) q3(q2−1). The proof involves a detailed study of Weierstraß points in characteristicp>0.—A characterization of the Fermat function fields in terms of their genus and their automorphism group is given.