Mathematics > Algebraic Geometry
[Submitted on 25 May 2018 (v1), last revised 17 Aug 2020 (this version, v3)]
Title:Computing square-free polarized abelian varieties over finite fields
View PDFAbstract:We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field $\mathbb{F}_q$ whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field $\mathbb{F}_p$ whose characteristic polynomial is square-free and does not have real roots. In the ordinary case we are also able to compute the polarizations and the group of automorphisms (of the polarized variety) and, when the polarization is principal, the period matrix.
Submission history
From: Stefano Marseglia [view email][v1] Fri, 25 May 2018 16:07:41 UTC (27 KB)
[v2] Tue, 29 Jan 2019 14:48:06 UTC (28 KB)
[v3] Mon, 17 Aug 2020 12:59:38 UTC (26 KB)
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