Product of Brauer--Manin obstructions for 0-cycles over number fields and function fields
Abstract
It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we prove that the existence of Brauer--Manin obstruction to Hasse principle for 0-cycles of degree 1 on the product of smooth (non-necessarily proper) varieties is equivalent to the simultaneous existence of such an obstruction on each factor. We also prove an analogous statement for smooth varieties defined over function fields of $\mathbb{C}((t))$-curves.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Analytic Number Theory Research
Publication details
- Journal / source
- ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
- Pages
- 14–14
- Publication date
- 2 March 2026
- Language
- EN