---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21751'
abstract:
- lang: eng
  text: 'We define a certain class of simple varieties over a field k by a constructive
    recipe and show how to control their (equivariant) truncating invariants. Consequently,
    we prove that on simple varieties: (i) if k = k and char k = p, the p-adic cyclotomic
    trace is an equivalence; (ii) if k = Q, the Goodwillie–Jones trace is an isomorphism
    in degree zero; (iii) we can control homotopy invariant K-theory KH, which is
    equivariantly formal and determined by its topological counterparts. Simple varieties
    are quite special, but encompass important singular examples appearing in geometric
    representation theory. We, in particular, show that both finite and affine Schubert
    varieties for GLn lie in this class, so all the above results hold for them. '
acknowledgement: "This work was supported by a DOC Fellowship of the Austrian Academy
  of Sciences at the Institute of Science and Technology Austria (ISTA) and by an
  Erasmus+ staff mobility training. It took place during the author’s visit to Laboratoire
  de Mathématiques d’Orsay in the course of his PhD at the Institute of Science and
  Technology Austria. First and foremost, I would like to thank Matthew Morrow for
  discussions, explanations and ideas without which this work would not have been
  carried out. I would further like to thank Brian Conrad for providing an amazing
  reference on projective cones in appropriate generality, to Vova Sosnilo for carefully
  discussing – among other things – the derived nilinvariance for quotients by any
  linearly reductive group, and to Adeel Khan, Timo Richarz, Matthias Wendt and Xinwen
  Zhu for helpful conversations\r\nabout the results. I would moreover like to thank
  the referee for the very useful comments."
article_number: rnag058
article_processing_charge: Yes (via OA deal)
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 localizing invariants of simple varieties. <i>International
    Mathematics Research Notices</i>. 2026;2026(7). doi:<a href="https://doi.org/10.1093/imrn/rnag058">10.1093/imrn/rnag058</a>
  apa: Löwit, J. (2026). Equivariant localizing invariants of simple varieties. <i>International
    Mathematics Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnag058">https://doi.org/10.1093/imrn/rnag058</a>
  chicago: Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.”
    <i>International Mathematics Research Notices</i>. Oxford University Press, 2026.
    <a href="https://doi.org/10.1093/imrn/rnag058">https://doi.org/10.1093/imrn/rnag058</a>.
  ieee: J. Löwit, “Equivariant localizing invariants of simple varieties,” <i>International
    Mathematics Research Notices</i>, vol. 2026, no. 7. Oxford University Press, 2026.
  ista: Löwit J. 2026. Equivariant localizing invariants of simple varieties. International
    Mathematics Research Notices. 2026(7), rnag058.
  mla: Löwit, Jakub. “Equivariant Localizing Invariants of Simple Varieties.” <i>International
    Mathematics Research Notices</i>, vol. 2026, no. 7, rnag058, Oxford University
    Press, 2026, doi:<a href="https://doi.org/10.1093/imrn/rnag058">10.1093/imrn/rnag058</a>.
  short: J. Löwit, International Mathematics Research Notices 2026 (2026).
corr_author: '1'
date_created: 2026-04-19T22:07:48Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-05-06T06:36:25Z
day: '01'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1093/imrn/rnag058
external_id:
  arxiv:
  - '2507.09392'
file:
- access_level: open_access
  checksum: 306f4567b7b2dcf38e23f7b55a27514e
  content_type: application/pdf
  creator: dernst
  date_created: 2026-05-06T06:35:05Z
  date_updated: 2026-05-06T06:35:05Z
  file_id: '21803'
  file_name: 2026_IMRN_Loewit.pdf
  file_size: 1663246
  relation: main_file
  success: 1
file_date_updated: 2026-05-06T06:35:05Z
has_accepted_license: '1'
intvolume: '      2026'
issue: '7'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
project:
- _id: 901e2a43-16d5-11f0-9cad-9cead34748d6
  grant_number: '27004'
  name: Arithmetic, geometry, topology and representation theory arising from the
    affine Grassmannian
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equivariant localizing invariants of simple varieties
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: 2026
year: '2026'
...