---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '22693'
abstract:
- lang: eng
  text: We study torus-equivariant algebraic K-theory of affine Schubert varieties
    in the perfect affine Grassmannians over Fp. We further compare it to the torus-equivariant
    Hochschild homology of perfect complexes, which has a geometric description in
    terms of global functions on certain fixed-point schemes. We prove that Fp-linearly,
    this comparison is an isomorphism. Our approach is quite constructive, resulting
    in new computations of these K-theory rings. We establish various structural results
    for equivariant perfect algebraic K-theory on the way; we believe these are of
    independent interest.
acknowledgement: "I would like to thank the following people for fruitful discussions,\r\nhelpful
  sanity checks or comments on previous drafts: Roman Bezrukavnikov, Jens Niklas Eberhardt,
  Mischa Elkner, Tamás Hausel, Andres Fernandez Herrero, Adeel Khan,\r\nBernhard Köck,
  Andrei Konovalov, Quoc Ho, Mirko Mauri, Matthew Morrow, Charanya\r\nRavi, Kamil
  Rychlewicz, Shyiu Shen, Vladimir Sosnilo, Georg Tamme, Xinwen Zhu. I\r\nwould further
  like to thank Marc Hoyois and the anonymous referee for spotting an error\r\nin
  a previous version.\r\nThis work was done during author’s PhD at the Institute of
  Science and Technology Austria (ISTA). It was funded by a DOC Fellowship of the
  Austrian Academy\r\nof Sciences and by the Austrian Science Fund (FWF) 10.55776/P35847.
  For open access\r\npurposes, the author has applied a CC BY public copyright license
  to any author-accepted\r\nmanuscript version arising from this submission."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Jakub
  full_name: Löwit, Jakub
  id: e3b80ae2-eb8e-11eb-b029-9aef4a9108a0
  last_name: Löwit
citation:
  ama: Löwit J. Equivariant K-theory, affine Grassmannian and perfection. <i>Documenta
    Mathematica</i>. 2026. doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a>
  apa: Löwit, J. (2026). Equivariant K-theory, affine Grassmannian and perfection.
    <i>Documenta Mathematica</i>. EMS Press. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a>
  chicago: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.”
    <i>Documenta Mathematica</i>. EMS Press, 2026. <a href="https://doi.org/10.4171/dm/1064">https://doi.org/10.4171/dm/1064</a>.
  ieee: J. Löwit, “Equivariant K-theory, affine Grassmannian and perfection,” <i>Documenta
    Mathematica</i>. EMS Press, 2026.
  ista: Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta
    Mathematica.
  mla: Löwit, Jakub. “Equivariant K-Theory, Affine Grassmannian and Perfection.” <i>Documenta
    Mathematica</i>, EMS Press, 2026, doi:<a href="https://doi.org/10.4171/dm/1064">10.4171/dm/1064</a>.
  short: J. Löwit, Documenta Mathematica (2026).
corr_author: '1'
das_tickbox: '0'
date_created: 2026-08-12T13:29:17Z
date_published: 2026-03-26T00:00:00Z
date_updated: 2026-08-13T07:00:17Z
day: '26'
ddc:
- '500'
department:
- _id: GradSch
- _id: TaHa
doi: 10.4171/dm/1064
external_id:
  arxiv:
  - '2409.18925'
has_accepted_license: '1'
keyword:
- equivariant algebraic K-theory
- perfection in positive characteristic
- affine Grassmannian
- affine Schubert varieties
- Dennis trace map
- equivariant Hochschild homology
- fixed-point schemes
- toric varieties
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.4171/DM/1064
mathsc:
- '19E08'
- 19L47
- 20G44
- 14G17
- 19D55
- 14F43
- 14L30
- 14D24
- 14M25
month: '03'
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
publication: Documenta Mathematica
publication_identifier:
  eissn:
  - 1431-0643
  issn:
  - 1431-0635
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
related_material:
  record:
  - id: '22694'
    relation: dissertation_contains
    status: for_moderation
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Equivariant K-theory, affine Grassmannian and perfection
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
year: '2026'
...