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Journal Article

#### Computing square-free polarized abelian varieties over finite fields

##### External Resource

https://doi.org/10.1090/mcom/3594

(Publisher version)

##### Fulltext (public)

arXiv:1805.10223.pdf

(Preprint), 270KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Marseglia, S. (2021). Computing square-free polarized abelian varieties over finite
fields.* Mathematics of Computation,* *90*(328), 953-971.
doi:10.1090/mcom/3594.

Cite as: http://hdl.handle.net/21.11116/0000-0007-AC18-D

##### 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.