Computing Néron–Severi groups and cycle class groups

DOI10.1112/S0010437X14007878zbMath1316.14017arXiv1210.3720MaRDI QIDQ5251377

Damiano Testa, Ronald van Luijk, Bjorn Poonen

Publication date: 20 May 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.3720

zbMATH Keywords

Tate conjectureNéron-Severi groupscycle class groups

Mathematics Subject Classification ID

Étale and other Grothendieck topologies and (co)homologies (14F20) Other nonalgebraically closed ground fields in algebraic geometry (14G27) Picard groups (14C22) Algebraic cycles (14C25) Global ground fields in algebraic geometry (14G25)

Related Items (14)

Pell surfaces ⋮ Explicit uniform bounds for Brauer groups of singular \(K3\) surfaces ⋮ The isomorphism problem of projective schemes and related algorithmic problems ⋮ Separation of periods of quartic surfaces ⋮ Explicit computation of a Galois representation attached to an eigenform over \(\mathrm{SL}_3\) from the \(\mathrm{H}_{\acute{\mathrm{e}}\mathrm{t}}^2\) of a surface ⋮ Computation of étale cohomology on curves in single exponential time ⋮ Bounds on the torsion subgroups of Néron–Severi groups ⋮ Arithmetic of K3 Surfaces ⋮ On the arithmetic of a family of degree - two K3 surfaces ⋮ A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants ⋮ Spectral Covers, Integrality Conditions, and Heterotic/F-theory Duality ⋮ ELLIPTIC K3 SURFACES ASSOCIATED WITH THE PRODUCT OF TWO ELLIPTIC CURVES: MORDELL–WEIL LATTICES AND THEIR FIELDS OF DEFINITION ⋮ Bounds on the torsion subgroup schemes of Néron-Severi group schemes ⋮ Commitment schemes and diophantine equations

Cites Work

• The Tate conjecture for \(K3\) surfaces over finite fields
• The Picard group of a \(K3\) surface and its reduction modulo \(p\)
• Néron-Severi groups under specialization
• Supersingular \(K3\) surfaces for large primes. With an Appendix by Andrew Snowden.
• The Tate conjecture for ordinary K 3 surfaces over finite fields
• An elliptic \(K3\) surface associated to Heron triangles
• \(K3\) surfaces with Picard number one and infinitely many rational points
• Tate's conjecture for \(K3\) surfaces of finite height
• Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes
• Relations between \(K_2\) and Galois cohomology
• On the Shafarevich and Tate conjectures for hyperkähler varieties
• Effective computation of Picard groups and Brauer-Manin obstructions of degree two \(K3\) surfaces over number fields
• On the Picard number of \(K3\) surfaces over number fields
• Algebraic cycles from a computational point of view
• On elliptic modular surfaces
• On the joints of Hensel rings
• On the computation of the Picard group for K3 surfaces
• Algebraic Groups Over Finite Fields
• Fujita's conjecture and Frobenius amplitude
• SHIODA-TATE FORMULA FOR AN ABELIAN FIBERED VARIETY AND APPLICATIONS
• An Explicit Algorithm for Computing the Picard Number of Certain Algebraic Surfaces
• Quantifier elimination in separably closed fields of finite imperfectness degree
• Elliptic K3 Surfaces with Geometric Mordell–Weil Rank 15
• Problèmes arithmétique et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps
• Sums of Betti numbers in arbitrary characteristic.

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