On a question of Colliot-Thélène on Chow group mod n

2019/06/19 by Kalyan Banerjee, Banerjee, Kalyan, Kalyan Chakraborty +1
Computer Science · Mathematics · #11G10 #14C25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1906.08233

openalex publication_date 2019/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we define the notion of Tate-Shafarevich group and Selmer group of the Chow group of an abelian variety defined over a number field. In this context we give positive answer to the question of Colliot-Thélène that the Chow group of zero cycles modulo n is finite over any number field.

Related

• Chow Groups of Abelian Varieties and Beilinson's Conjecture
• Complex varieties with infinite Chow groups modulo 2
• A filtration on the higher Chow group of zero cycles on an abelian variety
• Non-divisible cycles on products of very general Abelian varieties
• Zero-cycle groups on algebraic varieties