On the classification of commutative formal group laws over p-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices
We prove a finiteness theorem for the formal group laws, mentioned in the title, (theorem 1 and its corollary), thereby introducing a set of discrete invariants for the isomorphism classes of such group laws, called the jump sequence. An upper bound for the length of a jump sequence for Abelian varieties is given (theorem 4). As an illustration, we consider the simplest case of group laws having a jump sequence of minimal length 1, i.e. the case of potentially multiplicative formal group laws. Finally, we apply the results in order to obtain the unit root crystal and the \(\zeta\)-function for the family of hyperelliptic curves, defined over \(W(k)[\lambda]\) by the equation \(y^ 2=(x\) N-1)(x N-\(\lambda)\).
length of a jump sequence for Abelian varieties
scientific article; zbMATH DE number 4069069
scientific article