On Albanese torsors and the elementary obstruction

Abstract

We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given.

References in corpus (3)

• Duality of Albanese and Picard 1-motives
• On the Brauer-Manin obstruction for zero-cycles on curves
• The elementary obstruction and homogeneous spaces

Cited by in corpus (11)

• Galois sections for abelianized fundamental groups
• On abelian birational sections
• The cuspidalisation of sections of arithmetic fundamental groups II
• Supersolvable descent for rational points
• Homogeneous Fibrations over Curves
• The arithmetic Hodge Index Theorem and rigidity of dynamical systems over function fields
• La connexité rationnelle en arithmétique
• Moduli spaces and algebraic cycles in real algebraic geometry
• Derived Log Albanese Sheaves
• Fourier-Jacobi cycles and arithmetic relative trace formula (with an appendix by Chao Li and Yihang Zhu)
• Toric-friendly groups