On the classification of commutative formal group laws over p-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices
type: Item
instance of: scholarly article
title: On the classification of commutative formal group laws over p-Hilbert domains and a finiteness theorem for higher Hasse-Witt matrices
zbMATH Open document ID: 0655.14015
DOI: 10.1007/BF01180685
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174077
review text: 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-\(\lambda)\).
Mathematics Subject Classification ID: 14L05
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 4069069
zbMATH Keywords: higher Hasse-Witt matrices
zbMATH Keywords: formal group laws
zbMATH Keywords: length of a jump sequence for Abelian varieties
zbMATH Keywords: unit root crystal
zbMATH Keywords: hyperelliptic curves
author: Bert E. J. Ditters
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4069069