Cohen-Macaulay type of orders, generators and ideal classes

Publication date: 8 June 2022

Abstract: In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in 'etale algebras. We provide a bound for the type, and give formulas to compute it. We relate the type of the overorders of a given order to the size of minimal generating sets of its fractional ideals, generalizing known results for Gorenstein and Bass orders. Finally, we give a classification of the ideal classes with multiplicator ring of type

2

, with applications to the computations of the conjugacy classes of integral matrices and the isomorphism classes of abelian varieties over finite fields.

Has companion code repository: https://github.com/stmar89/alget

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Algebraic number theory computations (11Y40) Arithmetic ground fields for abelian varieties (14K15) Matrices of integers (15B36) Orders in separable algebras (16H10)

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