Cohen-Macaulay type of orders, generators and ideal classes

Abstract

In this paper we study the (Cohen-Macaulay) type of orders over Dedekind domains in étale 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.

accepted version

References in corpus (4)

• The trace of the canonical module
• Computing the ideal class monoid of an order
• Computing square-free polarized abelian varieties over finite fields
• Super-multiplicativity of ideal norms in number fields

Cited by in corpus (2)

• Local isomorphism classes of fractional ideals of orders in étale algebras
• Abelian varieties over finite fields and their groups of rational points