Local isomorphism classes of fractional ideals of orders in étale algebras

Stefano Marseglia

doi:10.1016/j.jalgebra.2025.02.030

Local isomorphism classes of fractional ideals of orders in étale algebras

Stefano Marseglia

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

Abstract

We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods.

Original language	English
Pages (from-to)	77-102
Number of pages	26
Journal	Journal of Algebra
Volume	673
DOIs	https://doi.org/10.1016/j.jalgebra.2025.02.030
Publication status	Published - 1 Jul 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Funding

The author is supported by NWO grant VI.Veni.202.107. The author thanks Jonas Bergstroem, Valentijn Karemaker and John Voight for comments on a preliminary version of the paper.

Funders	Funder number
NWO	VI.Veni.202.107

Keywords

Genus of an ideal
Ideal classes
Local isomorphism classes
Orders

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10.1016/j.jalgebra.2025.02.030Licence: CC BY

1-s2.0-S0021869325001097-mainFinal published version, 689 KBLicence: CC BY

Cite this

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abstract = "We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in {\'e}tale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods.",

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AB - We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in étale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a by-product, we obtain a recursive algorithm to compute representatives of the classes, which vastly outperforms previously known methods.

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ER -

Local isomorphism classes of fractional ideals of orders in étale algebras

Abstract

Bibliographical note

Funding

Keywords

Access to Document

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