{"id":"https://openalex.org/W7214739380","doi":"https://doi.org/10.48550/arxiv.2609.34589","title":"Structure of derived Hecke algebras with coefficients in torsion-free profinite rings","display_name":"Structure of derived Hecke algebras with coefficients in torsion-free profinite rings","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214739380","doi":"https://doi.org/10.48550/arxiv.2609.34589"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.34589","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34589","pdf_url":"https://arxiv.org/pdf/2609.34589","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/2609.34589","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048010769","display_name":"S. Kataoka","orcid":"https://orcid.org/0009-0001-0280-7671","observed_orcids":["https://orcid.org/0009-0001-0280-7671"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Kataoka, Shuta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048010769"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9140999913215637,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9140999913215637,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.023399999365210533,"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":0.02319999970495701,"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/continuous-cohomology","display_name":"continuous cohomology","score":0.871999979019165},{"id":"https://openalex.org/keywords/gl2-qp","display_name":"GL2(Qp)","score":0.7239999771118164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8690000176429749},{"id":"https://openalex.org/C67996461","wikidata":"https://www.wikidata.org/wiki/Q629933","display_name":"Subalgebra","level":3,"score":0.7867000102996826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.7009999752044678},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5077000260353088},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.48190000653266907},{"id":"https://openalex.org/C2781280181","wikidata":"https://www.wikidata.org/wiki/Q48970267","display_name":"Hecke algebra","level":3,"score":0.4602999985218048},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.45570001006126404},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.3995000123977661},{"id":"https://openalex.org/C14735163","wikidata":"https://www.wikidata.org/wiki/Q1428923","display_name":"Profinite group","level":3,"score":0.37220001220703125},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3434000015258789},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C118211362","wikidata":"https://www.wikidata.org/wiki/Q1203540","display_name":"Maximal ideal","level":3,"score":0.29989999532699585},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C53936288","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse limit","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C122129529","wikidata":"https://www.wikidata.org/wiki/Q2634828","display_name":"Inverse system","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C46467970","wikidata":"https://www.wikidata.org/wiki/Q1361055","display_name":"Discrete group","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2619999945163727},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.34589","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34589","pdf_url":"https://arxiv.org/pdf/2609.34589","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":"doi:10.48550/arxiv.2609.34589","doi":"https://doi.org/10.48550/arxiv.2609.34589","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.34589","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:2609.34589","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.34589","pdf_url":"https://arxiv.org/pdf/2609.34589","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/W7214739380.pdf","grobid_xml":"https://content.openalex.org/works/W7214739380.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W2512837087","https://openalex.org/W7164542767"],"related_works":["https://openalex.org/W7222541162","https://openalex.org/W6891958666","https://openalex.org/W2913970554","https://openalex.org/W7095883354","https://openalex.org/W2142345259","https://openalex.org/W2886642435","https://openalex.org/W2963336502","https://openalex.org/W2512837087","https://openalex.org/W2043217467","https://openalex.org/W2041678620"],"abstract_inverted_index":{"In":[0],"this":[1,58],"article,":[2],"we":[3],"study":[4],"derived":[5,30],"Hecke":[6,31],"algebras":[7,32,116],"with":[8,23,33,39,45,98,131],"coefficients":[9,34,132],"in":[10,35,75,133],"torsion-free":[11],"profinite":[12],"rings":[13,37],"regarded":[14],"as":[15],"discrete":[16],"rings.":[17],"We":[18,71,112],"compare":[19],"each":[20],"such":[21],"algebra":[22],"the":[24,29,54,73,102,110,114,118,124,143,147],"degreewise":[25],"inverse":[26],"limit":[27],"of":[28,43,77,142],"finite":[36,47],"and":[38,67,80,101,122,146],"its":[40,64,68],"subalgebra":[41,59],"consisting":[42],"elements":[44],"uniformly":[46],"double-coset":[48],"support.":[49],"Under":[50],"cohomological":[51],"comparison":[52],"hypotheses,":[53],"natural":[55],"map":[56],"to":[57],"has":[60],"image":[61],"given":[62],"by":[63,90],"degree-zero":[65],"part":[66],"positive-degree":[69,92],"torsion.":[70],"describe":[72],"kernel":[74],"terms":[76],"continuous":[78],"cohomology":[79],"prove":[81],"that":[82],"it":[83],"is":[84],"a":[85],"divisible":[86],"square-zero":[87],"ideal":[88],"annihilated":[89],"every":[91],"element.":[93],"These":[94],"comparisons":[95],"are":[96],"compatible":[97],"Yoneda":[99],"products,":[100],"action":[103],"on":[104],"torsion":[105],"Ext":[106],"classes":[107],"factors":[108],"through":[109],"image.":[111],"compute":[113],"resulting":[115],"for":[117,129,135],"additive":[119],"group":[120],"$\\mathbb{Q}_p$":[121],"determine":[123],"underlying":[125],"graded":[126],"abelian":[127],"groups":[128],"$(\\operatorname{GL}_2(\\mathbb{Q}_p),\\operatorname{GL}_2(\\mathbb{Z}_p))$":[130],"$\\mathbb{Z}_p$,":[134],"$p>3$.":[136],"The":[137],"examples":[138],"exhibit":[139],"distinct":[140],"effects":[141],"coefficient":[144],"topology":[145],"support":[148],"condition.":[149]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}