Cubic surfaces failing the integral Hasse principle

Publikation: Arbeitspapier/Preprint › Preprint

Autoren

  • Julian Lyczak
  • Vladimir Mitankin
  • H. Uppal

Organisationseinheiten

Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
PublikationsstatusVeröffentlicht - 16 Nov. 2023

Abstract

We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$.

Zitieren

Cubic surfaces failing the integral Hasse principle. / Lyczak, Julian; Mitankin, Vladimir; Uppal, H.
2023.

Publikation: Arbeitspapier/Preprint › Preprint

Lyczak, J, Mitankin, V & Uppal, H 2023 'Cubic surfaces failing the integral Hasse principle'.
Lyczak, J., Mitankin, V., & Uppal, H. (2023). Cubic surfaces failing the integral Hasse principle.
Lyczak J, Mitankin V, Uppal H. Cubic surfaces failing the integral Hasse principle. 2023 Nov 16.
Lyczak, Julian ; Mitankin, Vladimir ; Uppal, H. / Cubic surfaces failing the integral Hasse principle. 2023.
Download
@techreport{c4ca24e7d1fe4108b92de0a45f1954fb,
title = "Cubic surfaces failing the integral Hasse principle",
abstract = " We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$. ",
keywords = "math.NT, math.AG, 14G12 (primary), 11D25, 14G05, 14F22 (secondary)",
author = "Julian Lyczak and Vladimir Mitankin and H. Uppal",
note = "38 pages",
year = "2023",
month = nov,
day = "16",
language = "English",
type = "WorkingPaper",

}

Download

TY - UNPB

T1 - Cubic surfaces failing the integral Hasse principle

AU - Lyczak, Julian

AU - Mitankin, Vladimir

AU - Uppal, H.

N1 - 38 pages

PY - 2023/11/16

Y1 - 2023/11/16

N2 - We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$.

AB - We study the integral Brauer--Manin obstruction for affine diagonal cubic surfaces, which we employ to construct the first counterexamples to the integral Hasse principle in this setting. We then count in three natural ways how such counterexamples are distributed across the family of affine diagonal cubic surfaces and how often such surfaces satisfy integral strong approximation off $\infty$.

KW - math.NT

KW - math.AG

KW - 14G12 (primary), 11D25, 14G05, 14F22 (secondary)

M3 - Preprint

BT - Cubic surfaces failing the integral Hasse principle

ER -