---
OA_place: publisher
OA_type: hybrid
_id: '15338'
abstract:
- lang: eng
  text: We introduce a new class of generalised quadratic forms over totally real
    number fields, which is rich enough to capture the arithmetic of arbitrary systems
    of quadrics over the rational numbers. We explore this connection through a version
    of the Hardy–Littlewood circle method over number fields.
acknowledgement: The authors are grateful to Jayce Getz for asking questions that
  set this project in motion and to the anonymous referee for useful comments. T.B.
  was supported by a FWF grant (DOI 10.55776/P32428) and by a grant from the Institute
  for Advanced Study School of Mathematics. L.B.P. was partially supported by NSF
  DMS-2200470 and DMS-1652173, and thanks the Hausdorff Centre for Mathematics for
  hosting research visits.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
- first_name: Lillian B.
  full_name: Pierce, Lillian B.
  last_name: Pierce
- first_name: Damaris
  full_name: Schindler, Damaris
  last_name: Schindler
citation:
  ama: Browning TD, Pierce LB, Schindler D. Generalised quadratic forms over totally
    real number fields. <i>Journal of the Institute of Mathematics of Jussieu</i>.
    2024;23(6):2859-2912. doi:<a href="https://doi.org/10.1017/S1474748024000161">10.1017/S1474748024000161</a>
  apa: Browning, T. D., Pierce, L. B., &#38; Schindler, D. (2024). Generalised quadratic
    forms over totally real number fields. <i>Journal of the Institute of Mathematics
    of Jussieu</i>. Cambridge University Press. <a href="https://doi.org/10.1017/S1474748024000161">https://doi.org/10.1017/S1474748024000161</a>
  chicago: Browning, Timothy D, Lillian B. Pierce, and Damaris Schindler. “Generalised
    Quadratic Forms over Totally Real Number Fields.” <i>Journal of the Institute
    of Mathematics of Jussieu</i>. Cambridge University Press, 2024. <a href="https://doi.org/10.1017/S1474748024000161">https://doi.org/10.1017/S1474748024000161</a>.
  ieee: T. D. Browning, L. B. Pierce, and D. Schindler, “Generalised quadratic forms
    over totally real number fields,” <i>Journal of the Institute of Mathematics of
    Jussieu</i>, vol. 23, no. 6. Cambridge University Press, pp. 2859–2912, 2024.
  ista: Browning TD, Pierce LB, Schindler D. 2024. Generalised quadratic forms over
    totally real number fields. Journal of the Institute of Mathematics of Jussieu.
    23(6), 2859–2912.
  mla: Browning, Timothy D., et al. “Generalised Quadratic Forms over Totally Real
    Number Fields.” <i>Journal of the Institute of Mathematics of Jussieu</i>, vol.
    23, no. 6, Cambridge University Press, 2024, pp. 2859–912, doi:<a href="https://doi.org/10.1017/S1474748024000161">10.1017/S1474748024000161</a>.
  short: T.D. Browning, L.B. Pierce, D. Schindler, Journal of the Institute of Mathematics
    of Jussieu 23 (2024) 2859–2912.
corr_author: '1'
date_created: 2024-04-21T22:00:53Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-04T13:44:16Z
day: '01'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748024000161
external_id:
  arxiv:
  - '2212.11038'
  isi:
  - '001200337400001'
file:
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has_accepted_license: '1'
intvolume: '        23'
isi: 1
issue: '6'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '11'
oa: 1
oa_version: Published Version
page: 2859-2912
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
  eissn:
  - 1475-3030
  issn:
  - 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Generalised quadratic forms over totally real number fields
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 23
year: '2024'
...
---
_id: '10018'
abstract:
- lang: eng
  text: In order to study integral points of bounded log-anticanonical height on weak
    del Pezzo surfaces, we classify weak del Pezzo pairs. As a representative example,
    we consider a quartic del Pezzo surface of singularity type A1 + A3 and prove
    an analogue of Manin's conjecture for integral points with respect to its singularities
    and its lines.
acknowledgement: The first author was partly supported by grant DE 1646/4-2 of the
  Deutsche Forschungsgemeinschaft. The second author was partly supported by FWF grant
  P 32428-N35 and conducted part of this work as a guest at the Institut de Mathématiques
  de Jussieu–Paris Rive Gauche invited by Antoine Chambert-Loir and funded by DAAD.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Ulrich
  full_name: Derenthal, Ulrich
  last_name: Derenthal
- first_name: Florian Alexander
  full_name: Wilsch, Florian Alexander
  id: 560601DA-8D36-11E9-A136-7AC1E5697425
  last_name: Wilsch
  orcid: 0000-0001-7302-8256
citation:
  ama: Derenthal U, Wilsch FA. Integral points on singular del Pezzo surfaces. <i>Journal
    of the Institute of Mathematics of Jussieu</i>. 2024;23(3):1259-1294. doi:<a href="https://doi.org/10.1017/S1474748022000482">10.1017/S1474748022000482</a>
  apa: Derenthal, U., &#38; Wilsch, F. A. (2024). Integral points on singular del
    Pezzo surfaces. <i>Journal of the Institute of Mathematics of Jussieu</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/S1474748022000482">https://doi.org/10.1017/S1474748022000482</a>
  chicago: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
    Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>.
    Cambridge University Press, 2024. <a href="https://doi.org/10.1017/S1474748022000482">https://doi.org/10.1017/S1474748022000482</a>.
  ieee: U. Derenthal and F. A. Wilsch, “Integral points on singular del Pezzo surfaces,”
    <i>Journal of the Institute of Mathematics of Jussieu</i>, vol. 23, no. 3. Cambridge
    University Press, pp. 1259–1294, 2024.
  ista: Derenthal U, Wilsch FA. 2024. Integral points on singular del Pezzo surfaces.
    Journal of the Institute of Mathematics of Jussieu. 23(3), 1259–1294.
  mla: Derenthal, Ulrich, and Florian Alexander Wilsch. “Integral Points on Singular
    Del Pezzo Surfaces.” <i>Journal of the Institute of Mathematics of Jussieu</i>,
    vol. 23, no. 3, Cambridge University Press, 2024, pp. 1259–94, doi:<a href="https://doi.org/10.1017/S1474748022000482">10.1017/S1474748022000482</a>.
  short: U. Derenthal, F.A. Wilsch, Journal of the Institute of Mathematics of Jussieu
    23 (2024) 1259–1294.
corr_author: '1'
date_created: 2021-09-15T10:06:48Z
date_published: 2024-05-10T00:00:00Z
date_updated: 2025-04-15T07:39:01Z
day: '10'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.1017/S1474748022000482
external_id:
  arxiv:
  - '2109.06778'
  isi:
  - '000881319200001'
file:
- access_level: open_access
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  date_created: 2024-06-03T08:33:29Z
  date_updated: 2024-06-03T08:33:29Z
  file_id: '17102'
  file_name: 2024_JourMathJussieu_Derenthal.pdf
  file_size: 592305
  relation: main_file
  success: 1
file_date_updated: 2024-06-03T08:33:29Z
has_accepted_license: '1'
intvolume: '        23'
isi: 1
issue: '3'
keyword:
- Integral points
- del Pezzo surface
- universal torsor
- Manin’s conjecture
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 1259-1294
project:
- _id: 26AEDAB2-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P32428
  name: New frontiers of the Manin conjecture
publication: Journal of the Institute of Mathematics of Jussieu
publication_identifier:
  eissn:
  - '1475-3030 '
  issn:
  - 1474-7480
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Integral points on singular del Pezzo surfaces
tmp:
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  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2024'
...