2025/06/28 by Hui Zhang, Zhang, Hui
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2506.22980
openalex publication_date 2025/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Classical descent theory of Colliot-Thélène and Sansuc for rational points tells that, over a smooth variety X, the algebraic Brauer--Manin subset equals the descent obstruction subset defined by a universal torsor. Moreover, Harari shows that the Brauer--Manin subset equals the descent obstruction subset defined by torsors under connected linear groups. By using the abelian cohomology theory by Borovoi, we define abelianized descent obstructions for 0-cycles by torsors under connected linear groups. As an analogy, we show the equality between the Brauer--Manin obstruction and the abelianized descent obstruction for 0-cycles. We also show that the abelianized descent obstruction is the closure of the descent obstruction defined by Balestrieri and Berg when X is a projective rationally connected variety or a projective K3 surface.