{"id":"https://openalex.org/W7162773296","doi":"https://doi.org/10.48550/arxiv.2605.30285","title":"On the equivariant $KU_G$-local sphere for finite abelian groups","display_name":"On the equivariant $KU_G$-local sphere for finite abelian groups","publication_year":2026,"publication_date":"2026-05-28","ids":{"openalex":"https://openalex.org/W7162773296","doi":"https://doi.org/10.48550/arxiv.2605.30285"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.30285","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.30285","pdf_url":"https://arxiv.org/pdf/2605.30285","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2605.30285","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137344512","display_name":"Yingxin Li","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Yingxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5137344512"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10899","display_name":"Advanced Operator Algebra Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/equivariant-k-theory","display_name":"equivariant K-theory","score":0.9169999957084656},{"id":"https://openalex.org/keywords/equivariant-localization","display_name":"equivariant localization","score":0.6230000257492065},{"id":"https://openalex.org/keywords/finite-abelian-groups","display_name":"finite abelian groups","score":0.8510000109672546},{"id":"https://openalex.org/keywords/adams-operations","display_name":"Adams operations","score":0.8019999861717224},{"id":"https://openalex.org/keywords/sylow-p-subgroups","display_name":"Sylow p-subgroups","score":0.8759999871253967},{"id":"https://openalex.org/keywords/morava-k-theory","display_name":"Morava K-theory","score":0.7929999828338623},{"id":"https://openalex.org/keywords/cyclic-subgroups","display_name":"cyclic subgroups","score":0.6340000033378601}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8712999820709229},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.7444000244140625},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7135999798774719},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.6908000111579895},{"id":"https://openalex.org/C147688034","wikidata":"https://www.wikidata.org/wiki/Q1626416","display_name":"Homotopy group","level":3,"score":0.5893999934196472},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5644999742507935},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.5432999730110168},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4580000042915344},{"id":"https://openalex.org/C124535231","wikidata":"https://www.wikidata.org/wiki/Q1057919","display_name":"Sylow theorems","level":4,"score":0.4553000032901764},{"id":"https://openalex.org/C79236096","wikidata":"https://www.wikidata.org/wiki/Q14775269","display_name":"Homotopy category","level":3,"score":0.34200000762939453},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.3366999924182892},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.3314000070095062},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.2890999913215637},{"id":"https://openalex.org/C60394458","wikidata":"https://www.wikidata.org/wiki/Q4948983","display_name":"Bott periodicity theorem","level":5,"score":0.2590999901294708},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25529998540878296},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25440001487731934}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.30285","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.30285","pdf_url":"https://arxiv.org/pdf/2605.30285","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2605.30285","doi":"https://doi.org/10.48550/arxiv.2605.30285","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.30285","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2605.30285","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.30285","pdf_url":"https://arxiv.org/pdf/2605.30285","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7162773296.pdf","grobid_xml":"https://content.openalex.org/works/W7162773296.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W4223436249","https://openalex.org/W4320169231","https://openalex.org/W4395443252","https://openalex.org/W4416139367","https://openalex.org/W7154986036","https://openalex.org/W7164339270","https://openalex.org/W7203830565"],"related_works":["https://openalex.org/W4388826256","https://openalex.org/W4223436249","https://openalex.org/W2004352551","https://openalex.org/W7213394669","https://openalex.org/W2017539711","https://openalex.org/W4385894066","https://openalex.org/W2889607323","https://openalex.org/W2066800242","https://openalex.org/W2314032377","https://openalex.org/W333200590"],"abstract_inverted_index":{"We":[0],"study":[1],"$KU_G$-localization":[2],"for":[3,37,51,79,85],"finite":[4,8,81,88],"groups.":[5,83],"For":[6],"a":[7,66,100],"nilpotent":[9],"group":[10,89],"$G$,":[11,90],"we":[12,47,68,91],"identify":[13],"the":[14,18,26,34,38,44,55,61,71,94],"$KU_G/p$-local":[15],"sphere":[16],"as":[17,99],"fiber":[19],"of":[20,28,41,77,96,102,111,114],"an":[21,86],"Adams":[22],"operation,":[23],"and":[24,59],"reduce":[25],"computation":[27,36],"its":[29],"homotopy":[30,74],"Mackey":[31,75],"functors":[32,76],"to":[33,117],"corresponding":[35],"Sylow":[39],"$p$-subgroup":[40],"$G$.":[42],"At":[43],"prime":[45,116],"$2$,":[46],"compute":[48],"$\\underline\u03c0_*":[49],"L_{KU_G/2}S_G$":[50],"abelian":[52,82],"$2$-groups,":[53],"resolve":[54],"resulting":[56],"extension":[57],"problems,":[58],"determine":[60,70],"degree-zero":[62],"Hurewicz":[63],"image.":[64],"As":[65],"consequence,":[67],"completely":[69],"$\\mathbb":[72],"Z$-graded":[73],"$L_{KU_G}S_G$":[78],"all":[80],"Finally,":[84],"arbitrary":[87],"prove":[92],"that":[93],"$KU_G/p$-localization":[95],"$G$-spectra":[97],"splits":[98],"wedge":[101],"height-one":[103],"equivariant":[104],"Morava":[105],"$K$-localizations,":[106],"indexed":[107],"by":[108],"conjugacy":[109],"classes":[110],"cyclic":[112],"subgroups":[113],"order":[115],"$p$.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-05-30T00:00:00"}