Arithmetic of rational points and zero-cycles on products of Kummer varieties and K3 surfaces

Abstract

Let $k$ be a number field. 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 Kummer varieties over $k$. For example, for any Kummer variety $X$ over $k$, we show that if the Brauer-Manin obstruction is the only obstruction to the Hasse principle for rational points on $X$ over all finite extensions of $k$, then the ($2$-primary) Brauer-Manin obstruction is the only obstruction to the Hasse principle for zero-cycles of any given odd degree on $X$ over $k$. We also obtain similar results for products of Kummer varieties, K3 surfaces and rationally connected varieties.

arXiv comment16 pages. Corrected grant reference number and added journal reference and DOI. arXiv admin note: substantial text overlap with arXiv:1804.05819

References in corpus (8)

• Insufficiency of the Brauer-Manin obstruction applied to etale covers
• On the Brauer group of diagonal quartic surfaces
• Zéro-cycles sur les fibrations au-dessus d'une courbe de genre quelconque
• Finiteness theorems for K3 surfaces and abelian varieties of CM type
• Hasse principle for generalised Kummer varieties
• Transcendental Brauer groups of products of CM elliptic curves
• Second descent and rational points on Kummer varieties
• The Brauer-Manin obstruction for zero-cycles on K3 surfaces

Cited by in corpus (1)

• Arithmetic of Châtelet surface bundles revisited