{"id":"https://openalex.org/W7213499458","doi":"https://doi.org/10.48550/arxiv.2609.17621","title":"On motivic cohomology of commutative C*-algebras","display_name":"On motivic cohomology of commutative C*-algebras","publication_year":2026,"publication_date":"2026-09-14","ids":{"openalex":"https://openalex.org/W7213499458","doi":"https://doi.org/10.48550/arxiv.2609.17621"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.17621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17621","pdf_url":"https://arxiv.org/pdf/2609.17621","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":null,"license_id":null,"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/2609.17621","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128032158","display_name":"Ko Aoki","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Aoki, Ko","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5128032158"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":0.8241999745368958,"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":0.8241999745368958,"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":0.14110000431537628,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.01140000019222498,"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/motivic-cohomology","display_name":"motivic cohomology","score":0.9940000176429749},{"id":"https://openalex.org/keywords/commutative-c-algebras","display_name":"commutative C*-algebras","score":0.9850000143051147},{"id":"https://openalex.org/keywords/continuous-functions-on-compact-hausdorff-spaces","display_name":"continuous functions on compact Hausdorff spaces","score":0.9290000200271606},{"id":"https://openalex.org/keywords/algebraic-k-theory","display_name":"algebraic K-theory","score":0.9539999961853027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8495000004768372},{"id":"https://openalex.org/C84254916","wikidata":"https://www.wikidata.org/wiki/Q2981889","display_name":"Motivic cohomology","level":5,"score":0.6604999899864197},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6320000290870667},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.6093000173568726},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.5414000153541565},{"id":"https://openalex.org/C68365058","wikidata":"https://www.wikidata.org/wiki/Q1179446","display_name":"De Rham cohomology","level":4,"score":0.5110999941825867},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.4618000090122223},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.45890000462532043},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.4431000053882599},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C126867241","wikidata":"https://www.wikidata.org/wiki/Q3388699","display_name":"Cup product","level":5,"score":0.3804999887943268},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C2777041388","wikidata":"https://www.wikidata.org/wiki/Q6664297","display_name":"Local cohomology","level":3,"score":0.3671000003814697},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.36329999566078186},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3409000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.326200008392334},{"id":"https://openalex.org/C93067474","wikidata":"https://www.wikidata.org/wiki/Q1493952","display_name":"Sheaf cohomology","level":4,"score":0.3066999912261963},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2985000014305115},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.2930000126361847},{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.2574000060558319},{"id":"https://openalex.org/C78313660","wikidata":"https://www.wikidata.org/wiki/Q727659","display_name":"Commutative algebra","level":2,"score":0.2517000138759613}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.17621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17621","pdf_url":"https://arxiv.org/pdf/2609.17621","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:pure.mpg.de:item_3732042","doi":null,"is_oa":false,"landing_page_url":"https://hdl.handle.net/21.11116/0000-0013-9002-5","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.17621","doi":"https://doi.org/10.48550/arxiv.2609.17621","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.17621","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.17621","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.17621","pdf_url":"https://arxiv.org/pdf/2609.17621","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":null,"license_id":null,"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/W7213499458.pdf","grobid_xml":"https://content.openalex.org/works/W7213499458.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4386839767","https://openalex.org/W6910818288","https://openalex.org/W7165790557","https://openalex.org/W7212120673"],"related_works":["https://openalex.org/W1975899951","https://openalex.org/W7201841310","https://openalex.org/W603089199","https://openalex.org/W6960920274","https://openalex.org/W4404257431","https://openalex.org/W2520064750","https://openalex.org/W4404990870","https://openalex.org/W1975433563","https://openalex.org/W2071886435","https://openalex.org/W7099058139"],"abstract_inverted_index":{"Consider":[0],"the":[1,34,47],"ring":[2],"of":[3,27,40,52],"complex-valued":[4],"continuous":[5],"functions":[6],"on":[7],"a":[8,24],"compact":[9],"Hausdorff":[10],"space":[11],"$X$.":[12,53],"Corti\u00f1as--Thom":[13],"computed":[14],"its":[15],"nonpositive":[16],"algebraic":[17],"$K$-theory,":[18],"confirming":[19],"Rosenberg's":[20],"expectation.":[21],"We":[22],"give":[23],"motivic":[25,37],"refinement":[26],"their":[28],"result:":[29],"For":[30],"$i\\geq":[31],"2j\\geq":[32],"0$,":[33],"$i$th":[35,48],"integral":[36],"cohomology":[38,50],"group":[39,51],"weight":[41],"$j$":[42],"is":[43],"naturally":[44],"isomorphic":[45],"to":[46],"Betti":[49]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-18T00:00:00"}
