Jacobians in isogeny classes of abelian surfaces over finite fields

DOI10.5802/aif.2430zbMath1236.11058arXivmath/0607515OpenAlexW1611566840MaRDI QIDQ1010974

Christophe Ritzenthaler, Everett W. Howe, Enric Nart Viñals

Publication date: 7 April 2009

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607515

zbMATH Keywords

Jacobiancurvezeta functionabelian surfaceWeil polynomialWeil number

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Varieties over finite and local fields (11G25)

Related Items (16)

Optimal Encodings to Elliptic Curves of \(\boldsymbol{j}\)-Invariants 0, 1728 ⋮ Vanishing of hyperelliptic \(L\)-functions at the central point ⋮ Curves of medium genus with many points ⋮ Doubly isogenous genus-2 curves with 𝐷₄-action ⋮ Exceptional biases in counting primes over function fields ⋮ Computing genus 2 curves from invariants on the Hilbert moduli space ⋮ Jacobians in isogeny classes of supersingular abelian threefolds in characteristic 2 ⋮ Chebyshev's bias for products of irreducible polynomials ⋮ ON THE MERTENS CONJECTURE FOR ELLIPTIC CURVES OVER FINITE FIELDS ⋮ ON THE MERTENS CONJECTURE FOR FUNCTION FIELDS ⋮ Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus ⋮ On the number of points on abelian and Jacobian varieties over finite fields ⋮ Genus-2 curves and Jacobians with a given number of points ⋮ $p^k$-torsion of genus two curves over $\mathbb {F}_{p^m}$ ⋮ Explicit computations of Serre’s obstruction for genus-3 curves and application to optimal curves ⋮ Spanning the isogeny class of a power of an elliptic curve

Cites Work

• Corrigendum to: ``Improved upper bounds for the number of points on curves over finite fields
• On positive definite Hermitian forms
• Principally polarizable isogeny classes of Abelian surfaces over finite fields
• Nonsingular plane cubic curves over finite fields
• Galois Cohomology
• Which abelian surfaces are products of elliptic curves?
• Endomorphisms of Abelian varieties over finite fields
• Arithmetic of alternating forms and quaternion hermitian forms
• Arithmetic variety of moduli for genus two
• The number of curves of genus two with elliptic differentials.
• Weights in codes and genus 2 curves
• Abelian surfaces of GL₂-type as Jacobians of curves
• Non-existence of a curve over $\mathbb {F}_3$ of genus 5 with 14 rational points
• On the non-existence of certain curves of genus two
• Principally Polarized Ordinary Abelian Varieties Over Finite Fields
• Kernels of polarizations of abelian varieties over finite fields
• Large torsion subgroups of split Jacobians of curves of genus two or three
• Zeta Functions of Supersingular Curves of Genus 2
• Characteristic polynomials of automorphisms of hyperelliptic curves
• Abelian Surfaces over Finite Fields as Jacobians
• The first de Rham cohomology group and Dieudonné modules
• Abelian varieties over finite fields
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