Hasse-Witt matrices for the Fermat curves of prime degree
Let \(C\) be a smooth projective curve of genus \(g>0\) defined over an algebraically closed field of characteristic \(p>0\). The Hasse-Witt invariant \(r(C)\) of \(C\) is the maximum number of cyclic unramified independent extensions of degree \(p\) of the function field \(k(C)\). In this paper the Hasse-Witt invariants \(r(C_\ell)\) are computed for the family of curves \(C_\ell\) defined by the equation \(Y^\ell= F(X)\), where \(\ell\) is a prime and \(F(X)\in k[X]\) is a separable polynomial of degree \(n\). This family includes hyperelliptic curves \((\ell=2,\;n>2)\) and Fermat curves (when \(F(X)= X^\ell+1)\).
scientific article; zbMATH DE number 1054460