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arXiv · 2311.18571

Local isomorphism classes of fractional ideals of orders in \'etale algebras

Stefano Marseglia
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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 \'etale 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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Stefano Marseglia. 2023-11-30. Local isomorphism classes of fractional ideals of orders in \'etale algebras. https://doi.org/10.1016/j.jalgebra.2025.02.030

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