Quantitative arithmetic of diagonal degree 2 K3 surfaces

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Damián Gvirtz
  • Daniel Loughran
  • Masahiro Nakahara

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Externe Organisationen

  • University of Bath
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Details

OriginalspracheEnglisch
Seiten (von - bis)135-209
Seitenumfang75
FachzeitschriftMathematische Annalen
Jahrgang384
Ausgabenummer1-2
PublikationsstatusVeröffentlicht - Okt. 2022

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.

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Quantitative arithmetic of diagonal degree 2 K3 surfaces. / Gvirtz, Damián; Loughran, Daniel; Nakahara, Masahiro.
in: Mathematische Annalen, Jahrgang 384, Nr. 1-2, 10.2022, S. 135-209.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Gvirtz D, Loughran D, Nakahara M. Quantitative arithmetic of diagonal degree 2 K3 surfaces. Mathematische Annalen. 2022 Okt;384(1-2):135-209. doi: 10.48550/arXiv.1910.06257, 10.1007/s00208-021-02280-w
Gvirtz, Damián ; Loughran, Daniel ; Nakahara, Masahiro. / Quantitative arithmetic of diagonal degree 2 K3 surfaces. in: Mathematische Annalen. 2022 ; Jahrgang 384, Nr. 1-2. S. 135-209.
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