On supersingular abelian varieties of dimension two over finite fields

DOI10.1006/ffta.1996.0024zbMath0923.11091OpenAlexW1992986704MaRDI QIDQ1383511

Xing, Chaoping

Publication date: 26 April 1998

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/ffta.1996.0024

zbMATH Keywords

finite fieldscharacteristic polynomialsJacobians\(k\) rational pointssupersingular abelian varieties

Mathematics Subject Classification ID

Rational points (14G05) Abelian varieties of dimension (> 1) (11G10) Jacobians, Prym varieties (14H40) Curves over finite and local fields (11G20)

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On the parity of supersingular Weil polynomials ⋮ Endomorphism algebras of QM abelian surfaces ⋮ Every finite abelian group is the group of rational points of an ordinary abelian variety over 𝔽₂, 𝔽₃ and 𝔽₅ ⋮ Fibre products of supersingular curves and the enumeration of irreducible polynomials with prescribed coefficients ⋮ Groups of points on abelian threefolds over finite fields ⋮ Classification of characteristic polynomials of simple supersingular abelian varieties over finite fields ⋮ Group structures of elementary supersingular abelian varieties over finite fields. ⋮ The groups of points on abelian varieties over finite fields ⋮ Supersingular hyperelliptic curves of genus 2 over finite fields ⋮ Varieties over finite fields: quantitative theory ⋮ Trisection for supersingular genus \(2\) curves in characteristic \(2\) ⋮ Abelian Surfaces over Finite Fields as Jacobians ⋮ Abelian surfaces over finite fields with prescribed groups ⋮ Weight of duals of BCH codes and exponential sums

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