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  Computing square-free polarized abelian varieties over finite fields

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

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Item Permalink: https://hdl.handle.net/21.11116/0000-0007-AC18-D Version Permalink: https://hdl.handle.net/21.11116/0000-000D-F6DB-7
Genre: Journal Article

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arXiv:1805.10223.pdf (Preprint), 270KB
 
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https://doi.org/10.1090/mcom/3594 (Publisher version)
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 Creators:
Marseglia, Stefano1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Number Theory
 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.

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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
 Pages: 19
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1805.10223
DOI: 10.1090/mcom/3594
 Degree: -

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Title: Mathematics of Computation
  Abbreviation : Math. Comp.
Source Genre: Journal
 Creator(s):
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Publ. Info: American Mathematical Society
Pages: - Volume / Issue: 90 (328) Sequence Number: - Start / End Page: 953 - 971 Identifier: -