Computing Néron-Severi groups and cycle class groups

Abstract

Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron-Severi group of any smooth projective geometrically integral variety, and also the rank of the group of numerical equivalence classes of codimension p cycles for any p.

22 pages; to appear in Compositio Math

References in corpus (3)

• The Tate conjecture for K3 surfaces over finite fields
• Supersingular K3 surfaces for large primes
• Calculabilité de la cohomologie étale modulo l

Cited by in corpus (9)

• A numerical transcendental method in algebraic geometry
• Effective bounds for Brauer groups of Kummer surfaces over number fields
• Calculabilité de la cohomologie étale modulo l
• Elliptic K3 surfaces associated with the product of two elliptic curves: Mordell-Weil lattices and their fields of definition
• A Brauer-Siegel theorem for Fermat surfaces over finite fields
• Effective obstruction to lifting Tate classes from positive characteristic
• Separation of periods of quartic surfaces
• The isomorphism problem of projective schemes and related algorithmic problems
• Arithmetic Deformation of Line Bundles