---
_id: '14239'
abstract:
- lang: eng
  text: "Given a resolution of rational singularities  π:X~→X  over a field of characteristic
    zero, we use a Hodge-theoretic argument to prove that the image of the functor
    \ Rπ∗:Db(X~)→Db(X)\r\n  between bounded derived categories of coherent sheaves
    generates  Db(X)\r\n  as a triangulated category. This gives a weak version of
    the Bondal–Orlov localization conjecture [BO02], answering a question from [PS21].
    The same result is established more generally for proper (not necessarily birational)
    morphisms  π:X~→X , with  X~\r\n  smooth, satisfying  Rπ∗(OX~)=OX ."
acknowledgement: "We thank Agnieszka Bodzenta-Skibińska, Paolo Cascini, Wahei Hara,
  Sándor Kovács, Alexander Kuznetsov, Mircea Musta  ă, Nebojsa Pavic, Pavel Sechin,
  and Michael Wemyss for discussions and e-mail correspondence. We also thank the
  anonymous referee for the helpful comments. M.M. was supported by the Institute
  of Science and Technology Austria. This project has received funding from the European
  Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
  grant agreement no. 101034413. E.S. was partially supported by the EPSRC grant EP/T019379/1
  “Derived categories and algebraic K-theory of singularities”, and by the ERC Synergy
  grant “Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler
  Varieties.”\r\n\r\n"
article_number: e66
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Mirko
  full_name: Mauri, Mirko
  id: 2cf70c34-09c1-11ed-bd8d-c34fac206130
  last_name: Mauri
- first_name: Evgeny
  full_name: Shinder, Evgeny
  last_name: Shinder
citation:
  ama: Mauri M, Shinder E. Homological Bondal-Orlov localization conjecture for rational
    singularities. <i>Forum of Mathematics, Sigma</i>. 2023;11. doi:<a href="https://doi.org/10.1017/fms.2023.65">10.1017/fms.2023.65</a>
  apa: Mauri, M., &#38; Shinder, E. (2023). Homological Bondal-Orlov localization
    conjecture for rational singularities. <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press. <a href="https://doi.org/10.1017/fms.2023.65">https://doi.org/10.1017/fms.2023.65</a>
  chicago: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization
    Conjecture for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>. Cambridge
    University Press, 2023. <a href="https://doi.org/10.1017/fms.2023.65">https://doi.org/10.1017/fms.2023.65</a>.
  ieee: M. Mauri and E. Shinder, “Homological Bondal-Orlov localization conjecture
    for rational singularities,” <i>Forum of Mathematics, Sigma</i>, vol. 11. Cambridge
    University Press, 2023.
  ista: Mauri M, Shinder E. 2023. Homological Bondal-Orlov localization conjecture
    for rational singularities. Forum of Mathematics, Sigma. 11, e66.
  mla: Mauri, Mirko, and Evgeny Shinder. “Homological Bondal-Orlov Localization Conjecture
    for Rational Singularities.” <i>Forum of Mathematics, Sigma</i>, vol. 11, e66,
    Cambridge University Press, 2023, doi:<a href="https://doi.org/10.1017/fms.2023.65">10.1017/fms.2023.65</a>.
  short: M. Mauri, E. Shinder, Forum of Mathematics, Sigma 11 (2023).
corr_author: '1'
date_created: 2023-08-27T22:01:16Z
date_published: 2023-08-03T00:00:00Z
date_updated: 2025-04-14T07:54:52Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1017/fms.2023.65
ec_funded: 1
external_id:
  arxiv:
  - '2212.06786'
  isi:
  - '001041926700001'
file:
- access_level: open_access
  checksum: c36241750cc5cb06890aec0ecdfee626
  content_type: application/pdf
  creator: dernst
  date_created: 2023-09-05T06:43:11Z
  date_updated: 2023-09-05T06:43:11Z
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  file_name: 2023_ForumMathematics_Mauri.pdf
  file_size: 280865
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file_date_updated: 2023-09-05T06:43:11Z
has_accepted_license: '1'
intvolume: '        11'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Forum of Mathematics, Sigma
publication_identifier:
  eissn:
  - 2050-5094
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homological Bondal-Orlov localization conjecture for rational singularities
tmp:
  image: /images/cc_by.png
  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: 11
year: '2023'
...