Zero-cycles in families of rationally connected varieties

2022/11/08 by Morten Lüders, Lüders, Morten
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2211.04300

openalex publication_date 2022/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally connected. We further extend this result to certain higher Chow groups and develop conjectures in the non-smooth case. Our main results generalise a result of Kollár [31].

Related

• Rigidity for relative 0-cycles
• On zero-cycles of varieties over Laurent fields
• Zero-cycle groups on algebraic varieties
• Zero cycles on rationally connected varieties over Laurent fields
• Specialization of zero cycles