{"id":"https://openalex.org/W7203869276","doi":"https://doi.org/10.48550/arxiv.2608.20171","title":"Koszul cohomology of \u010cech cohomology modules","display_name":"Koszul cohomology of \u010cech cohomology modules","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203869276","doi":"https://doi.org/10.48550/arxiv.2608.20171"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.20171","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20171","pdf_url":"https://arxiv.org/pdf/2608.20171","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.20171","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025991082","display_name":"Maryam Jahangiri","orcid":"https://orcid.org/0000-0002-4198-9295","observed_orcids":["https://orcid.org/0000-0002-4198-9295"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jahangiri, Maryam","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5025991082"],"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9984999895095825,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9984999895095825,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.00019999999494757503,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.00019999999494757503,"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/koszul-cohomology","display_name":"Koszul cohomology","score":0.9860000014305115},{"id":"https://openalex.org/keywords/serre-subcategories","display_name":"Serre subcategories","score":0.8069999814033508},{"id":"https://openalex.org/keywords/regular-sequences","display_name":"regular sequences","score":0.6100000143051147},{"id":"https://openalex.org/keywords/local-cohomology","display_name":"local cohomology","score":0.7149999737739563},{"id":"https://openalex.org/keywords/double-complexes","display_name":"double complexes","score":0.6589999794960022},{"id":"https://openalex.org/keywords/spectral-sequences","display_name":"spectral sequences","score":0.9660000205039978},{"id":"https://openalex.org/keywords/commutative-noetherian-rings","display_name":"commutative Noetherian rings","score":0.9100000262260437},{"id":"https://openalex.org/keywords/ext-functor","display_name":"Ext functor","score":0.5080000162124634}],"concepts":[{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.8618999719619751},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8550999760627747},{"id":"https://openalex.org/C178609977","wikidata":"https://www.wikidata.org/wiki/Q3503315","display_name":"Spectral sequence","level":3,"score":0.6536999940872192},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5936999917030334},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.574999988079071},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.5590999722480774},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.41429999470710754},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.40860000252723694},{"id":"https://openalex.org/C2777041388","wikidata":"https://www.wikidata.org/wiki/Q6664297","display_name":"Local cohomology","level":3,"score":0.4041999876499176},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36480000615119934},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.3391999900341034},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.32330000400543213},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.32170000672340393},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3075999915599823},{"id":"https://openalex.org/C2780212368","wikidata":"https://www.wikidata.org/wiki/Q7840150","display_name":"Triangulated category","level":4,"score":0.2874999940395355},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C74196217","wikidata":"https://www.wikidata.org/wiki/Q1095535","display_name":"\u010cech cohomology","level":5,"score":0.2802000045776367},{"id":"https://openalex.org/C155751095","wikidata":"https://www.wikidata.org/wiki/Q1408937","display_name":"Group cohomology","level":3,"score":0.26339998841285706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.20171","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20171","pdf_url":"https://arxiv.org/pdf/2608.20171","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.2608.20171","doi":"https://doi.org/10.48550/arxiv.2608.20171","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.20171","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:2608.20171","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.20171","pdf_url":"https://arxiv.org/pdf/2608.20171","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203869276.pdf","grobid_xml":"https://content.openalex.org/works/W7203869276.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3118949010","https://openalex.org/W2594644911","https://openalex.org/W2980951898","https://openalex.org/W3011690664","https://openalex.org/W1964402640","https://openalex.org/W2889605449","https://openalex.org/W2952951355","https://openalex.org/W1802164691","https://openalex.org/W4387664898","https://openalex.org/W2130425396"],"abstract_inverted_index":{"Let":[0,26],"$R$":[1],"be":[2,9,16,29],"a":[3,17,30],"commutative":[4],"Noetherian":[5],"ring,":[6],"let":[7,14],"$\\mathbf{x}=x_1,\\ldots,x_n$":[8],"an":[10],"$R$-regular":[11],"sequence,":[12],"and":[13,53],"$\\mathbf{y}=y_1,\\ldots,y_m$":[15],"sequence":[18],"of":[19,21,33,36],"elements":[20],"$R$.":[22],"Put":[23],"$I=(\\mathbf":[24],"y)$.":[25],"$\\mathcal":[27],"S$":[28],"Serre":[31],"subcategory":[32],"the":[34,40,45,54,63],"category":[35],"$R$-modules.":[37],"We":[38],"consider":[39],"double":[41,70],"complex":[42,56],"obtained":[43],"from":[44],"Koszul":[46],"co-complex":[47],"with":[48,57,68],"respect":[49,58],"to":[50,59],"$\\mathbf":[51,60],"x$":[52],"\u010cech":[55],"y$.":[61],"Using":[62],"two":[64],"spectral":[65],"sequences":[66],"associated":[67],"this":[69],"complex,":[71],"we":[72],"prove":[73],"that":[74],"\\[":[75,86],"Ext_R^i(R/(\\mathbf":[76],"x),H_I^j(R))\\in\\mathcal":[77],"S":[78,89],"\\quad\\text{for":[79,90],"all":[80,91],"}i,j\\in":[81],"\\mathbb":[82],"N_0":[83],"\\]":[84,94],"implies":[85],"H_I^j(R/(\\mathbf":[87],"x))\\in\\mathcal":[88],"}j\\in\\mathbb":[92],"N_0.":[93]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-22T00:00:00"}
