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Local isomorphism classes of fractional ideals of orders in étale algebras (2311.18571v2)
Published 30 Nov 2023 in math.NT and math.RA
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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