{"id":"https://openalex.org/W7214707380","doi":"https://doi.org/10.48550/arxiv.2609.32287","title":"Bernstein--Sato ideals might not be linear","display_name":"Bernstein--Sato ideals might not be linear","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214707380","doi":"https://doi.org/10.48550/arxiv.2609.32287"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32287","pdf_url":"https://arxiv.org/pdf/2609.32287","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/2609.32287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153445309","display_name":"Lei Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wu, Lei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153445309"],"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":0.4675000011920929,"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":0.4675000011920929,"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":0.45559999346733093,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.039400000125169754,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.859000027179718},{"id":"https://openalex.org/keywords/linear-polynomials","display_name":"linear polynomials","score":0.5730000138282776},{"id":"https://openalex.org/keywords/rational-coefficients","display_name":"rational coefficients","score":0.875},{"id":"https://openalex.org/keywords/zero-locus","display_name":"zero locus","score":0.6060000061988831},{"id":"https://openalex.org/keywords/polynomial-ideals","display_name":"polynomial ideals","score":0.5090000033378601}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8014000058174133},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7832000255584717},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5526000261306763},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.505299985408783},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4657999873161316},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3662000000476837},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.35199999809265137},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31869998574256897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31679999828338623},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.28209999203681946},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.259799987077713}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32287","pdf_url":"https://arxiv.org/pdf/2609.32287","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.2609.32287","doi":"https://doi.org/10.48550/arxiv.2609.32287","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32287","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.32287","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32287","pdf_url":"https://arxiv.org/pdf/2609.32287","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214707380.pdf","grobid_xml":"https://content.openalex.org/works/W7214707380.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W2961324757","https://openalex.org/W3133450139","https://openalex.org/W4415161600","https://openalex.org/W7128064456"],"related_works":["https://openalex.org/W7220671877","https://openalex.org/W2948222788","https://openalex.org/W1629159307","https://openalex.org/W2031528609","https://openalex.org/W6964327346","https://openalex.org/W3049457854","https://openalex.org/W7204492855","https://openalex.org/W7197345829","https://openalex.org/W7081566766","https://openalex.org/W1502047093"],"abstract_inverted_index":{"Let":[0],"$F=(f_1,\\dots,f_r)$":[1],"be":[2],"a":[3],"family":[4],"of":[5,23,29,38,64],"nonzero":[6],"polynomials":[7,31],"on":[8],"$\\mathbb":[9],"C^n$.":[10],"More":[11],"than":[12],"ten":[13],"years":[14],"ago,":[15],"Budur":[16],"conjectured":[17],"that":[18,50,60],"$B_F$,":[19],"the":[20,36,56,61],"Bernstein--Sato":[21],"ideal":[22],"$F$,":[24],"is":[25],"generated":[26],"by":[27],"products":[28],"linear":[30],"with":[32],"rational":[33],"coefficients.":[34],"With":[35],"aid":[37],"AI,":[39],"we":[40],"construct":[41],"two":[42],"counterexamples":[43],"to":[44],"Budur's":[45],"conjecture.":[46],"The":[47],"examples":[48],"indicate":[49],"main":[51],"results":[52],"in":[53,68],"[Wu26]":[54],"provide":[55],"optimal":[57],"linearity":[58],"properties":[59],"zero":[62],"locus":[63],"Bernstein-Sato":[65],"ideals":[66],"satisfies":[67],"general.":[69]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
