Quantitative arithmetic of diagonal degree $2$ K3 surfaces

Autor:	Gvirtz-Chen, Damián, Loughran, Daniel, Nakahara, Masahiro
Rok vydání:	2019
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 14G05 (primary) 14F22 (secondary)
Druh dokumentu:	Working Paper
Popis:	In this paper we study the existence of rational points for the family of K3 surfaces over $\mathbb{Q}$ given by $$w^2 = A_1x_1^6 + A_2x_2^6 + A_3x_3^6.$$ When the coefficients are ordered by height, we show that the Brauer group is almost always trivial, and find the exact order of magnitude of surfaces for which there is a Brauer-Manin obstruction to the Hasse principle. Our results show definitively that K3 surfaces can have a Brauer-Manin obstruction to the Hasse principle that is only explained by odd order torsion. Comment: 57 pages. To appear in Mathematische Annalen
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.06257 Zobrazit plný text záznamu View this record from Arxiv