Divisibility Results for zero-cycles

2020/04/10 by Gazaki, Evangelia, Hiranouchi, Toshiro
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2004.05255

Abstract

Let X be a product of smooth projective curves over a finite unramified extension k of ℚ_p. Suppose that the Albanese variety of X has good reduction and that X has a k-rational point. We propose the following conjecture. The kernel of the Albanese map CH₀(X)⁰\rightarrowAlb_X(k) is p-divisible. When p is an odd prime, we prove this conjecture for a large family of products of elliptic curves and certain principal homogeneous spaces of abelian varieties. Using this, we provide some evidence for a local-to-global conjecture for zero-cycles of Colliot-Thélène and Sansuc (\citeColliot-Thelene/Sansuc1981), and Kato and Saito (\citeKato/Saito1986).

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