Arithmetic of rational points and zero-cycles on Kummer varieties

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 $k$.

arXiv commentThe contents of this paper have now been merged into arXiv:1805.12538v2

References in corpus (4)

• On the Brauer group of diagonal quartic surfaces
• Finiteness theorems for K3 surfaces and abelian varieties of CM type
• Transcendental Brauer groups of products of CM elliptic curves
• The Brauer-Manin obstruction for zero-cycles on K3 surfaces