Computing square-free polarized abelian varieties over finite fields

Stefano Marseglia

doi:10.1090/mcom/3594

Computing square-free polarized abelian varieties over finite fields

Stefano Marseglia

Matematiska institutionen, Stockholms universitet

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field Fq whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field Fp 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.

Original language	English
Pages (from-to)	953-971
Number of pages	19
Journal	Mathematics of Computation
Volume	90
Issue number	328
DOIs	https://doi.org/10.1090/mcom/3594
Publication status	Published - Mar 2021
Externally published	Yes

Bibliographical note

Funding Information:
The author would like to thank Jonas Bergstr?om for helpful discussions and Rachel Newton and Christophe Ritzhentaler for comments on a previous version of the paper, which is part of the author?s Ph.D thesis [Mar18a]. The author would also like to express his gratitude to the Max Planck Institute for Mathematics in Bonn for their hospitality. The author thanks the anonymous reviewer of Mathematics of Computation for useful comments and suggestions.

Publisher Copyright:
© 2020. American Mathematical Society. All Rights Reserved.

Keywords

math.AG
math.NT
14K15 (Primary) 14G15, 11G10, 11G25, 14-04 (Secondary)

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10.1090/mcom/3594

1805.10223v3Submitted manuscript, 269 KB

Cite this

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Computing square-free polarized abelian varieties over finite fields

Abstract

Bibliographical note

Keywords

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