[{"project":[{"name":"Arithmetic, geometry, topology and representation theory arising from the affine Grassmannian","grant_number":"27004","_id":"901e2a43-16d5-11f0-9cad-9cead34748d6"}],"publication_status":"published","file_date_updated":"2026-05-06T06:35:05Z","file":[{"creator":"dernst","file_name":"2026_IMRN_Loewit.pdf","date_created":"2026-05-06T06:35:05Z","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"21803","date_updated":"2026-05-06T06:35:05Z","relation":"main_file","checksum":"306f4567b7b2dcf38e23f7b55a27514e","file_size":1663246}],"oa_version":"Published Version","has_accepted_license":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0","full_name":"Löwit, Jakub","last_name":"Löwit","first_name":"Jakub"}],"volume":2026,"intvolume":"      2026","article_type":"original","_id":"21751","year":"2026","ddc":["510"],"arxiv":1,"day":"01","OA_type":"hybrid","quality_controlled":"1","department":[{"_id":"TaHa"}],"scopus_import":"1","type":"journal_article","publisher":"Oxford University Press","OA_place":"publisher","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.","language":[{"iso":"eng"}],"issue":"7","title":"Equivariant localizing invariants of simple varieties","month":"04","article_number":"rnag058","date_published":"2026-04-01T00:00:00Z","date_updated":"2026-05-06T06:36:25Z","oa":1,"citation":{"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>.","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>","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>","short":"J. Löwit, International Mathematics Research Notices 2026 (2026).","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.","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>."},"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. "}],"publication":"International Mathematics Research Notices","status":"public","date_created":"2026-04-19T22:07:48Z","external_id":{"arxiv":["2507.09392"]},"PlanS_conform":"1","corr_author":"1","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"doi":"10.1093/imrn/rnag058","article_processing_charge":"Yes (via OA deal)"}]