The number of varieties in a family which contain a rational pointCitation formats

  • Authors:
  • Daniel Loughran

Standard

The number of varieties in a family which contain a rational point. / Loughran, Daniel.

In: Journal of the European Mathematical Society, Vol. 20, No. 10, 2018, p. 2539-2588.

Research output: Contribution to journalArticlepeer-review

Harvard

Loughran, D 2018, 'The number of varieties in a family which contain a rational point', Journal of the European Mathematical Society, vol. 20, no. 10, pp. 2539-2588. https://doi.org/10.4171/JEMS/818

APA

Loughran, D. (2018). The number of varieties in a family which contain a rational point. Journal of the European Mathematical Society, 20(10), 2539-2588. https://doi.org/10.4171/JEMS/818

Vancouver

Loughran D. The number of varieties in a family which contain a rational point. Journal of the European Mathematical Society. 2018;20(10):2539-2588. https://doi.org/10.4171/JEMS/818

Author

Loughran, Daniel. / The number of varieties in a family which contain a rational point. In: Journal of the European Mathematical Society. 2018 ; Vol. 20, No. 10. pp. 2539-2588.

Bibtex

@article{086b17b491c946dd8ffb2a3702b62af6,
title = "The number of varieties in a family which contain a rational point",
abstract = "We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.",
keywords = "Brauer groups, Families of varieties, Rational points, Toric varieties",
author = "Daniel Loughran",
note = "Publisher Copyright: {\textcopyright} European Mathematical Society 2018. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2018",
doi = "10.4171/JEMS/818",
language = "English",
volume = "20",
pages = "2539--2588",
journal = "Journal of the European Mathematical Society",
issn = "1435-9855",
publisher = "European Mathematical Society",
number = "10",

}

RIS

TY - JOUR

T1 - The number of varieties in a family which contain a rational point

AU - Loughran, Daniel

N1 - Publisher Copyright: © European Mathematical Society 2018. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2018

Y1 - 2018

N2 - We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.

AB - We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer group elements. Using harmonic analysis on toric varieties, we provide a positive answer to a question of Serre on such counting functions in some cases. We also formulate some conjectures on generalisations of Serre's problem.

KW - Brauer groups

KW - Families of varieties

KW - Rational points

KW - Toric varieties

U2 - 10.4171/JEMS/818

DO - 10.4171/JEMS/818

M3 - Article

VL - 20

SP - 2539

EP - 2588

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

SN - 1435-9855

IS - 10

ER -