Cohen-Macaulay type of orders, generators and ideal classes
Commutative Algebra
2025-02-28 v2 Number Theory
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 , with applications to the computations of the conjugacy classes of integral matrices and the isomorphism classes of abelian varieties over finite fields.
Cite
@article{arxiv.2206.03758,
title = {Cohen-Macaulay type of orders, generators and ideal classes},
author = {Stefano Marseglia},
journal= {arXiv preprint arXiv:2206.03758},
year = {2025}
}
Comments
accepted version