---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '19071'
abstract:
- lang: eng
  text: "An action of a complex reductive group G on a smooth projective variety X
    is regular when all regular unipotent elements in G act with finitely many fixed
    points. Then the complex G\r\n-equivariant cohomology ring of X is isomorphic
    to the coordinate ring of a certain regular fixed point scheme. Examples include
    partial flag varieties, smooth Schubert varieties and Bott-Samelson varieties.
    We also show that a more general version of the fixed point scheme allows a generalisation
    to GKM spaces, such as toric varieties."
acknowledgement: 'The first author was supported by an FWF grant “Geometry of the
  top of the nilpotent cone” number P 35847. The second author was supported by an
  Austrian Academy of Sciences DOC Fellowship “Topology of open smooth varieties with
  a torus action”. '
article_number: '1'
article_processing_charge: Yes
article_type: original
arxiv: 1
author:
- first_name: Tamás
  full_name: Hausel, Tamás
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
  orcid: 0000-0002-9582-2634
- first_name: Kamil P
  full_name: Rychlewicz, Kamil P
  id: 85A07246-A8BF-11E9-B4FA-D9E3E5697425
  last_name: Rychlewicz
citation:
  ama: Hausel T, Rychlewicz KP. Spectrum of equivariant cohomology as a fixed point
    scheme. <i>Epijournal de Geometrie Algebrique</i>. 2025;9. doi:<a href="https://doi.org/10.46298/epiga.2025.12591">10.46298/epiga.2025.12591</a>
  apa: Hausel, T., &#38; Rychlewicz, K. P. (2025). Spectrum of equivariant cohomology
    as a fixed point scheme. <i>Epijournal de Geometrie Algebrique</i>. EPI Sciences.
    <a href="https://doi.org/10.46298/epiga.2025.12591">https://doi.org/10.46298/epiga.2025.12591</a>
  chicago: Hausel, Tamás, and Kamil P Rychlewicz. “Spectrum of Equivariant Cohomology
    as a Fixed Point Scheme.” <i>Epijournal de Geometrie Algebrique</i>. EPI Sciences,
    2025. <a href="https://doi.org/10.46298/epiga.2025.12591">https://doi.org/10.46298/epiga.2025.12591</a>.
  ieee: T. Hausel and K. P. Rychlewicz, “Spectrum of equivariant cohomology as a fixed
    point scheme,” <i>Epijournal de Geometrie Algebrique</i>, vol. 9. EPI Sciences,
    2025.
  ista: Hausel T, Rychlewicz KP. 2025. Spectrum of equivariant cohomology as a fixed
    point scheme. Epijournal de Geometrie Algebrique. 9, 1.
  mla: Hausel, Tamás, and Kamil P. Rychlewicz. “Spectrum of Equivariant Cohomology
    as a Fixed Point Scheme.” <i>Epijournal de Geometrie Algebrique</i>, vol. 9, 1,
    EPI Sciences, 2025, doi:<a href="https://doi.org/10.46298/epiga.2025.12591">10.46298/epiga.2025.12591</a>.
  short: T. Hausel, K.P. Rychlewicz, Epijournal de Geometrie Algebrique 9 (2025).
corr_author: '1'
date_created: 2025-02-23T23:01:56Z
date_published: 2025-02-03T00:00:00Z
date_updated: 2025-04-15T06:31:58Z
day: '03'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.46298/epiga.2025.12591
external_id:
  arxiv:
  - '2212.11836'
file:
- access_level: open_access
  checksum: 3915c6f117461502f7103878460428df
  content_type: application/pdf
  creator: dernst
  date_created: 2025-02-25T06:53:27Z
  date_updated: 2025-02-25T06:53:27Z
  file_id: '19085'
  file_name: 2025_Epiga_Hausel.pdf
  file_size: 3276395
  relation: main_file
  success: 1
file_date_updated: 2025-02-25T06:53:27Z
has_accepted_license: '1'
intvolume: '         9'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-sa/4.0/
month: '02'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
  grant_number: P35847
  name: Geometry of the tip of the global nilpotent cone
- _id: 34cd0f74-11ca-11ed-8bc3-bf0492a14a24
  grant_number: '26525'
  name: Topology of open smooth varieties with a torus action
publication: Epijournal de Geometrie Algebrique
publication_identifier:
  eissn:
  - 2491-6765
publication_status: published
publisher: EPI Sciences
quality_controlled: '1'
related_material:
  record:
  - id: '17157'
    relation: earlier_version
    status: public
scopus_import: '1'
status: public
title: Spectrum of equivariant cohomology as a fixed point scheme
tmp:
  image: /images/cc_by_sa.png
  legal_code_url: https://creativecommons.org/licenses/by-sa/4.0/legalcode
  name: Creative Commons Attribution-ShareAlike 4.0 International Public License (CC
    BY-SA 4.0)
  short: CC BY-SA (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9
year: '2025'
...