On zero-cycles of varieties over Laurent fields

2024/02/22 by Jan de Lange, Lange, Jan
Computer Science · Mathematics · #14C25 #14M22 #14M25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2402.14406

openalex publication_date 2024/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize a recent result of Pavic--Schreieder regarding the surjectivity of the obstruction morphism defined in [PS23]. As a consequence of this result, we show that geometrically (retract) rational varieties over a Laurent field of characteristic 0, which admit a strictly semi-stable model, have trivial Chow group of zero-cycles. Our key new ingredient comes from toric geometry.

Related

• Zero-cycles in families of rationally connected varieties
• Zero cycles on rationally connected varieties over Laurent fields
• Zero-cycle groups on algebraic varieties
• A Finiteness theorem for zero-cycles over p-adic fields
• Groupe de Chow des zéro-cycles sur les variétés p-adiques