{"id":"https://openalex.org/W7203598968","doi":"https://doi.org/10.48550/arxiv.2608.14283","title":"On Takahashi's descent question about dominant local rings","display_name":"On Takahashi's descent question about dominant local rings","publication_year":2026,"publication_date":"2026-08-14","ids":{"openalex":"https://openalex.org/W7203598968","doi":"https://doi.org/10.48550/arxiv.2608.14283"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.14283","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14283","pdf_url":"https://arxiv.org/pdf/2608.14283","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/2608.14283","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159847534","display_name":"Jian Liu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Liu, Jian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5159847534"],"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.7670999765396118,"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":0.7670999765396118,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.094200000166893,"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"}},{"id":"https://openalex.org/T11703","display_name":"Rings, Modules, and Algebras","score":0.08609999716281891,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/commutative-noetherian-local-rings","display_name":"commutative Noetherian local rings","score":0.9340000152587891},{"id":"https://openalex.org/keywords/dominance","display_name":"dominance","score":0.4650000035762787},{"id":"https://openalex.org/keywords/singularity-category","display_name":"singularity category","score":0.8199999928474426},{"id":"https://openalex.org/keywords/idempotent-completion","display_name":"idempotent completion","score":0.9959999918937683},{"id":"https://openalex.org/keywords/compact-stars","display_name":"compact stars","score":0.7599999904632568},{"id":"https://openalex.org/keywords/injective-modules","display_name":"injective modules","score":0.9940000176429749}],"concepts":[{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.7825999855995178},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7039999961853027},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.6728000044822693},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.534600019454956},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5084999799728394},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.5026999711990356},{"id":"https://openalex.org/C46333567","wikidata":"https://www.wikidata.org/wiki/Q2138875","display_name":"Regular local ring","level":4,"score":0.486299991607666},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.45649999380111694},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3817000091075897},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33469998836517334},{"id":"https://openalex.org/C2986090443","wikidata":"https://www.wikidata.org/wiki/Q77870413","display_name":"Local structure","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C84583765","wikidata":"https://www.wikidata.org/wiki/Q1868517","display_name":"Local field","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.3025999963283539},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C151913843","wikidata":"https://www.wikidata.org/wiki/Q3454555","display_name":"Dominance (genetics)","level":3,"score":0.26409998536109924},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.14283","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14283","pdf_url":"https://arxiv.org/pdf/2608.14283","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.2608.14283","doi":"https://doi.org/10.48550/arxiv.2608.14283","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.14283","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:2608.14283","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.14283","pdf_url":"https://arxiv.org/pdf/2608.14283","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":[{"id":"https://openalex.org/G2136804278","display_name":null,"funder_award_id":"12401046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320325599","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09"},{"id":"https://openalex.org/F4320338388","display_name":"Eurostars","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203598968.pdf","grobid_xml":"https://content.openalex.org/works/W7203598968.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4414878359","https://openalex.org/W4415023773","https://openalex.org/W7135066996","https://openalex.org/W7202174049"],"related_works":["https://openalex.org/W4214636648","https://openalex.org/W1600090509","https://openalex.org/W7096811741","https://openalex.org/W7219275409","https://openalex.org/W2004711180","https://openalex.org/W1488091669","https://openalex.org/W4414878359","https://openalex.org/W7204483347","https://openalex.org/W2740630554","https://openalex.org/W1562902488"],"abstract_inverted_index":{"This":[0],"article":[1],"studies":[2],"dominant":[3],"local":[4,17,23],"rings,":[5,24],"a":[6,15],"notion":[7],"introduced":[8],"by":[9],"Takahashi.":[10],"We":[11],"prove":[12],"that,":[13],"for":[14],"flat":[16],"homomorphism":[18],"R-->S":[19],"between":[20],"commutative":[21],"noetherian":[22],"dominance":[25],"descends":[26],"from":[27],"S":[28],"to":[29],"R,":[30],"thereby":[31],"answering":[32],"Takahashi's":[33],"descent":[34],"question":[35],"affirmatively.":[36],"The":[37],"proof":[38],"makes":[39],"use":[40],"of":[41,44,48,55,62,65],"Krause's":[42],"realization":[43],"the":[45,49,53,59],"idempotent":[46],"completion":[47],"singularity":[50],"category":[51,61],"as":[52],"subcategory":[54],"compact":[56],"objects":[57],"in":[58],"homotopy":[60],"acyclic":[63],"complexes":[64],"injective":[66],"modules.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-18T00:00:00"}
