Quantitative arithmetic of diagonal degree 2 K3 surfaces

authored by

Damián Gvirtz, Daniel Loughran, Masahiro Nakahara

Abstract

In this paper we study the existence of rational points for the family of K3 surfaces over Q given by

w2 = A1x6 1 + A2 x6 2 + A3x6 3 .

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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Bath

Type

Article

Journal

Mathematische Annalen

Volume

384

Pages

135-209

No. of pages

75

ISSN

0025-5831

Publication date

10.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

https://doi.org/10.48550/arXiv.1910.06257 (Access: Open)
https://doi.org/10.1007/s00208-021-02280-w (Access: Closed)