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Computing abelian varieties over finite fields isogenous to a power
Stockholm University, Faculty of Science, Department of Mathematics. Universiteit Utrecht, The Netherlands.ORCID iD: 0000-0003-1648-4938
Number of Authors: 12019 (English)In: Research in Number Theory, ISSN 2522-0160, Vol. 5, no 4, article id 35Article in journal (Refereed) Published
Abstract [en]

In this paper we give a module-theoretic description of the isomorphism classes of abelian varieties A isogenous to Br, where the characteristic polynomial g of Frobenius of B is an ordinary square-free q-Weil polynomial, for a power q of a prime p, or a square-free p-Weil polynomial with no real roots. Under some extra assumptions on the polynomial g we give an explicit description of all the isomorphism classes which can be computed in terms of fractional ideals of an order in a finite product of number fields. In the ordinary case, we also give a module-theoretic description of the polarizations of A.

Place, publisher, year, edition, pages
2019. Vol. 5, no 4, article id 35
Keywords [en]
Abelian varieties, Finite fields, Polarizations, Bass orders
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-176679DOI: 10.1007/s40993-019-0174-xISI: 000493759500001OAI: oai:DiVA.org:su-176679DiVA, id: diva2:1377974
Available from: 2019-12-13 Created: 2019-12-13 Last updated: 2019-12-13Bibliographically approved

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