Details
| Original language | English |
|---|---|
| Pages (from-to) | 135-209 |
| Number of pages | 75 |
| Journal | Mathematische Annalen |
| Volume | 384 |
| Issue number | 1-2 |
| Publication status | Published - Oct 2022 |
Abstract
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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In: Mathematische Annalen, Vol. 384, No. 1-2, 10.2022, p. 135-209.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Quantitative arithmetic of diagonal degree 2 K3 surfaces
AU - Gvirtz, Damián
AU - Loughran, Daniel
AU - Nakahara, Masahiro
N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022/10
Y1 - 2022/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85116885776&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1910.06257
DO - 10.48550/arXiv.1910.06257
M3 - Article
VL - 384
SP - 135
EP - 209
JO - Mathematische Annalen
JF - Mathematische Annalen
SN - 0025-5831
IS - 1-2
ER -