Cohen-Macaulay type of orders, generators and ideal classes

Stefano Marseglia

doi:10.1016/j.jalgebra.2024.05.051

Cohen-Macaulay type of orders, generators and ideal classes

Stefano Marseglia^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	247-276
Number of pages	30
Journal	Journal of Algebra
Volume	658
DOIs	https://doi.org/10.1016/j.jalgebra.2024.05.051
Publication status	Published - 15 Nov 2024

Bibliographical note

Publisher Copyright:
© 2024 The Author(s)

Funding

The author is grateful to Jonas Bergstr\u00F6m and Hendrik W. Lenstra Jr. for useful discussions and comments on a preliminary version of the paper. The author thanks Carel Faber for useful comments. The author was supported by NWO grant VI.Veni.202.107.

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	VI.Veni.202.107

Keywords

Cohen-Macaulay type
Generators
Ideal classes
Orders

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10.1016/j.jalgebra.2024.05.051Licence: CC BY

1-s2.0-S0021869324003351-mainFinal published version, 503 KBLicence: CC BY

Cite this

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Cohen-Macaulay type of orders, generators and ideal classes

Abstract

Bibliographical note

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Keywords

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