Chow Groups of Abelian Varieties and Beilinson's Conjecture

2016/12/11 by Bogdan Zavyalov, Zavyalov, Bogdan
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1612.03489

openalex publication_date 2016/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we introduce the property AA of a subsemigroup of the endomorphism semigroup of an abelian variety, which holds for semigroup of endomorphisms of an abelian variety defined over a number field, and show that the orbit of any cycle under a semigroup with property AA in the Chow group ⊗\Q has finite dimensional span.

Related

• On a question of Colliot-Thélène on Chow group mod n
• An exposition on finite dimensionality of Chow groups
• Beilinson-Tate cycles on semiabelian varieties
• Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori
• About Chow groups of certain hyperkähler varieties with non-symplectic automorphisms