Quantitative arithmetic of diagonal degree 2 K3 surfaces

verfasst von

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.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Externe Organisation(en)

University of Bath

Typ

Artikel

Journal

Mathematische Annalen

Band

384

Seiten

135-209

Anzahl der Seiten

75

ISSN

0025-5831

Publikationsdatum

10.2022

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Mathematik (insg.)

Elektronische Version(en)

https://doi.org/10.48550/arXiv.1910.06257 (Zugang: Offen)
https://doi.org/10.1007/s00208-021-02280-w (Zugang: Geschlossen)