Cohen-Macaulay type of orders, generators and ideal classes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912248576868352 |
|---|---|
| author | Marseglia, Stefano |
| author_facet | Marseglia, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03758 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cohen-Macaulay type of orders, generators and ideal classes Marseglia, Stefano Commutative Algebra Number Theory 16H10, 11Y40, 13H10, 15B36, 14K15 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. |
| title | Cohen-Macaulay type of orders, generators and ideal classes |
| topic | Commutative Algebra Number Theory 16H10, 11Y40, 13H10, 15B36, 14K15 |
| url | https://arxiv.org/abs/2206.03758 |