Connected Part of the Covariant Tate p-Divisible Group and the zeta-Function of the Family of Hyperelliptic Curves y sup 2 = 1 + mu(chi sup N) Modulo Various Primes

摘要

The authors determine for mu epsilon W (k), k an arbitrary finite field of characteristics p > 2 with p sup a elements the explicit action of the sigma - linear Frobenius (F sub p) on the connected component of the covariant Tate module of the Jacobian variety for the family of curves, defined by y squared = 1 + mu(chi sup N). From this, various objects, such as the decomposition into isogeny factors and the characteristic polynomial of the linear Frobenius pi= (F sub p, sup a) can be studied.