{"id":"https://openalex.org/W7204924388","doi":"https://doi.org/10.48550/arxiv.2608.29044","title":"Examples of nontrivial presilting objects in a singularity category","display_name":"Examples of nontrivial presilting objects in a singularity category","publication_year":2026,"publication_date":"2026-08-29","ids":{"openalex":"https://openalex.org/W7204924388","doi":"https://doi.org/10.48550/arxiv.2608.29044"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.29044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29044","pdf_url":"https://arxiv.org/pdf/2608.29044","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/2608.29044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015883919","display_name":"Changchang Xi","orcid":"https://orcid.org/0000-0002-6710-095X","observed_orcids":["https://orcid.org/0000-0002-6710-095X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xi, Changchang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5148934962","display_name":"Jinbi Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Jinbi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9980000257492065,"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":0.0008999999845400453,"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/singularity-category","display_name":"singularity category","score":0.9890000224113464},{"id":"https://openalex.org/keywords/finite-dimensional-algebras","display_name":"finite-dimensional algebras","score":0.972000002861023},{"id":"https://openalex.org/keywords/positive-characteristic","display_name":"positive characteristic","score":0.9750000238418579},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.7900000214576721},{"id":"https://openalex.org/keywords/triangulated-categories","display_name":"triangulated categories","score":0.6269999742507935}],"concepts":[{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.8199999928474426},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7797999978065491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7099999785423279},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6664000153541565},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5419999957084656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.536300003528595},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4823000133037567},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C207769094","wikidata":"https://www.wikidata.org/wiki/Q4245771","display_name":"Singularity theory","level":3,"score":0.3970000147819519},{"id":"https://openalex.org/C71383303","wikidata":"https://www.wikidata.org/wiki/Q1876526","display_name":"Essential singularity","level":3,"score":0.2992999851703644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2904999852180481},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.2842999994754791},{"id":"https://openalex.org/C191413488","wikidata":"https://www.wikidata.org/wiki/Q1892554","display_name":"Operator algebra","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2653000056743622},{"id":"https://openalex.org/C143904861","wikidata":"https://www.wikidata.org/wiki/Q2297037","display_name":"Isolated singularity","level":3,"score":0.2517000138759613},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.25029999017715454},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.2502000033855438}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.29044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29044","pdf_url":"https://arxiv.org/pdf/2608.29044","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.2608.29044","doi":"https://doi.org/10.48550/arxiv.2608.29044","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.29044","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:2608.29044","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.29044","pdf_url":"https://arxiv.org/pdf/2608.29044","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":[{"id":"https://openalex.org/G4021989058","display_name":null,"funder_award_id":"12401038","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204924388.pdf","grobid_xml":"https://content.openalex.org/works/W7204924388.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4396561659","https://openalex.org/W4406053738","https://openalex.org/W4366328535","https://openalex.org/W7207860195","https://openalex.org/W7098378985","https://openalex.org/W2910755577","https://openalex.org/W4287183720","https://openalex.org/W3014299177","https://openalex.org/W2962727514","https://openalex.org/W2952055394"],"abstract_inverted_index":{"It":[0],"was":[1],"conjectured":[2],"that":[3],"no":[4],"presilting":[5],"objects":[6],"exist":[7],"in":[8],"the":[9,20],"singularity":[10],"category":[11],"of":[12,36],"a":[13,17],"finite-dimensional":[14],"algebra":[15],"over":[16,34],"field":[18],"except":[19],"zero":[21],"object.":[22],"In":[23],"this":[24,30],"note,":[25],"we":[26],"give":[27],"counterexamples":[28],"to":[29],"conjecture":[31],"for":[32],"algebras":[33],"fields":[35],"positive":[37],"characteristic.":[38]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-02T00:00:00"}