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arXiv · 1804.05819

Arithmetic of rational points and zero-cycles on Kummer varieties

Francesca Balestrieri·Rachel Newton
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Abstract

Let $k$ be a number field, let $X$ be a Kummer variety over $k$, and let $\delta$ be an odd integer. In the spirit of a result by Yongqi Liang, we relate the arithmetic of rational points over finite extensions of $k$ to that of zero-cycles over $k$ for $X$. For example, we show that if the Brauer-Manin obstruction is the only obstruction to the existence of rational points on $X$ over all finite extensions of $k$, then the $2$-primary Brauer-Manin obstruction is the only obstruction to the existence of a zero-cycle of degree $\delta$ on $X$ over $k$.

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Francesca Balestrieri, Rachel Newton. 2018-04-16. Arithmetic of rational points and zero-cycles on Kummer varieties. https://arxiv.org/abs/1804.05819

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