Year: 2026
Type: preprint
Abstract: For a quasi-projective smooth geometrically integral variety $X$ over a number field, we prove that the Brauer-Manin obstruction for its symmetric powers coincides with the obstruction coming from $X$. As a consequence, Brauer-Manin obstruction for the symmetric powers cannot provide new cohomological obstruction to weak approximation of zero-cycles for $X$. The key intermediate ingredients are a Dold-Thom type result for Brauer groups and a precise descent formula for adelic points.
Source: arXiv (Cornell University)
Authors: Cao, Yang, Zhou, Lin
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G5089335471
OpenAlex ID: W7222917138