Computing square-free polarized abelian varieties over finite fields
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Abstract:
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.References
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Additional Information
- Stefano Marseglia
- Affiliation: Matematiska institutionen, Stockholms universitet, Sweden
- Address at time of publication: Mathematical Institute, Utrecht University, The Netherlands
- MR Author ID: 1347583
- ORCID: 0000-0003-1648-4938
- Email: s.marseglia@uu.nl
- Received by editor(s): January 21, 2020
- Received by editor(s) in revised form: August 1, 2020
- Published electronically: November 16, 2020
- © Copyright 2020 American Mathematical Society
- Journal: Math. Comp. 90 (2021), 953-971
- MSC (2020): Primary 14K15; Secondary 14G15, 11G10, 11G25, 14-04
- DOI: https://doi.org/10.1090/mcom/3594
- MathSciNet review: 4194169