{"supplementarymaterial":"no","type":"journal_article","date_created":"2026-08-12T13:29:17Z","_id":"22693","das_tickbox":"0","ddc":["500"],"arxiv":1,"article_processing_charge":"Yes (in subscription journal)","corr_author":"1","PlanS_conform":"1","researchdata_availability":"no","date_updated":"2026-08-13T07:00:17Z","doi":"10.4171/dm/1064","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"abstract":[{"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.","lang":"eng"}],"date_published":"2026-03-26T00:00:00Z","title":"Equivariant K-theory, affine Grassmannian and perfection","main_file_link":[{"open_access":"1","url":"https://doi.org/10.4171/DM/1064"}],"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"],"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.","language":[{"iso":"eng"}],"OA_place":"publisher","publication":"Documenta Mathematica","publication_status":"epub_ahead","oa":1,"author":[{"id":"e3b80ae2-eb8e-11eb-b029-9aef4a9108a0","full_name":"Löwit, Jakub","first_name":"Jakub","last_name":"Löwit"}],"project":[{"name":"Geometry of the tip of the global nilpotent cone","grant_number":"P35847","_id":"34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3"}],"quality_controlled":"1","oa_version":"Published Version","year":"2026","OA_type":"hybrid","has_accepted_license":"1","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"related_material":{"record":[{"id":"22694","relation":"dissertation_contains","status":"for_moderation"}]},"status":"public","scopus_import":"1","publisher":"EMS Press","day":"26","article_type":"original","external_id":{"arxiv":["2409.18925"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"GradSch"},{"_id":"TaHa"}],"month":"03","citation":{"short":"J. Löwit, Documenta Mathematica (2026).","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>.","ista":"Löwit J. 2026. Equivariant K-theory, affine Grassmannian and perfection. Documenta Mathematica.","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>","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>","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."},"mathsc":["19E08","19L47","20G44","14G17","19D55","14F43","14L30","14D24","14M25"]}