Computing the endomorphism ring of an ordinary abelian surface over a finite field

DOI10.1016/j.jnt.2019.01.013zbMath1470.11175arXiv1810.12270OpenAlexW2963188210MaRDI QIDQ2420398

Caleb Springer

Publication date: 6 June 2019

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12270

zbMATH Keywords

algorithmfinite fieldabelian varietyisogenycomputationideal class groupendomorphism ring

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Varieties over finite and local fields (11G25)

Related Items (2)

On the computation of the endomorphism rings of abelian surfaces ⋮ The structure of the group of rational points of an abelian variety over a finite field

Uses Software

• Magma
• AVIsogenies

Cites Work

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• Computing $(\ell ,\ell )$-isogenies in polynomial time on Jacobians of genus $2$ curves
• Computing endomorphism rings of abelian varieties of dimension two
• Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
• Abelian varieties over finite fields
• On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field

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