Quantitative arithmetic of diagonal degree 2 K3 surfaces

Damián Gvirtz, Daniel Loughran, Masahiro Nakahara

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Abstract

In this paper we study the existence of rational points for the family of K3 surfaces over Q given by w2=A1x16+A2x26+A3x36.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.

Original languageEnglish
Pages (from-to)1-75
JournalMathematische Annalen
Volume384
Early online date11 Oct 2021
DOIs
Publication statusPublished - 31 Oct 2022

ASJC Scopus subject areas

  • Mathematics(all)

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