{"id":"https://openalex.org/W7207860195","doi":"https://doi.org/10.48550/arxiv.2609.02023","title":"A negative answer to a question on tilting objects and two-term complexes","display_name":"A negative answer to a question on tilting objects and two-term complexes","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207860195","doi":"https://doi.org/10.48550/arxiv.2609.02023"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02023","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02023","pdf_url":"https://arxiv.org/pdf/2609.02023","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/2609.02023","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094208344","display_name":"Jing He","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Jing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5085299791","display_name":"Panyue Zhou","orcid":"https://orcid.org/0000-0003-3763-0690","observed_orcids":["https://orcid.org/0000-0003-3763-0690"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Panyue","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":0.9984999895095825,"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":0.9984999895095825,"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":0.0003000000142492354,"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":9.999999747378752e-05,"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/silting-objects","display_name":"silting objects","score":0.9549999833106995},{"id":"https://openalex.org/keywords/tilting-complexes","display_name":"tilting complexes","score":0.8619999885559082},{"id":"https://openalex.org/keywords/triangulated-categories","display_name":"triangulated categories","score":0.847000002861023},{"id":"https://openalex.org/keywords/finite-dimensional-algebras","display_name":"finite-dimensional algebras","score":0.675000011920929},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.6150000095367432}],"concepts":[{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.7508999705314636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6449000239372253},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.5929999947547913},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.5755000114440918},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5342000126838684},{"id":"https://openalex.org/C2780212368","wikidata":"https://www.wikidata.org/wiki/Q7840150","display_name":"Triangulated category","level":4,"score":0.4844000041484833},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41819998621940613},{"id":"https://openalex.org/C153778094","wikidata":"https://www.wikidata.org/wiki/Q357858","display_name":"Adjoint functors","level":3,"score":0.4131999909877777},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35600000619888306},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.32339999079704285},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.3183000087738037},{"id":"https://openalex.org/C2777601897","wikidata":"https://www.wikidata.org/wiki/Q3409113","display_name":"Presentation (obstetrics)","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30379998683929443},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.29100000858306885},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2671999931335449},{"id":"https://openalex.org/C156163052","wikidata":"https://www.wikidata.org/wiki/Q5379515","display_name":"Enriched category","level":3,"score":0.26159998774528503},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02023","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02023","pdf_url":"https://arxiv.org/pdf/2609.02023","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.2609.02023","doi":"https://doi.org/10.48550/arxiv.2609.02023","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02023","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:2609.02023","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02023","pdf_url":"https://arxiv.org/pdf/2609.02023","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207860195.pdf","grobid_xml":"https://content.openalex.org/works/W7207860195.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W4417064402"],"related_works":["https://openalex.org/W4394654735","https://openalex.org/W4311649458","https://openalex.org/W3195431608","https://openalex.org/W4408362329","https://openalex.org/W1998072847","https://openalex.org/W4417064402","https://openalex.org/W3113712461","https://openalex.org/W2080428639","https://openalex.org/W4285563186","https://openalex.org/W2948316874"],"abstract_inverted_index":{"Let":[0],"$M$":[1],"be":[2,26,40],"a":[3,46,68,75,90,96],"silting":[4,69,92],"object":[5,70,77],"in":[6,53],"an":[7,58],"idempotent":[8],"complete":[9],"algebraic":[10],"triangulated":[11],"category":[12],"$\\mathcal":[13],"T$.":[14],"Put":[15],"$B={\\rm":[16],"End}_{\\mathcal":[17],"T}(M)$,":[18],"and":[19,74],"let":[20],"$\\mathbb{P}_M\\colon":[21],"{\\rm":[22,83],"pr}(M)\\to":[23],"K^{[-1,0]}({\\rm":[24],"proj}B)$":[25],"the":[27,54],"presentation":[28],"functor":[29],"associated":[30],"with":[31],"$M$.":[32],"It":[33],"was":[34],"recently":[35],"asked":[36],"whether":[37],"$\\mathbb{P}_M(T)$":[38,88],"must":[39],"tilting":[41,47,76,97],"whenever":[42],"$T\\in{\\rm":[43],"pr}(M)$":[44,79],"is":[45,89],"object.":[48],"We":[49],"answer":[50],"this":[51],"question":[52],"negative":[55],"by":[56],"giving":[57],"explicit":[59],"finite-dimensional":[60],"example.":[61],"Namely,":[62],"for":[63,80],"$$":[64,82],"\u039b=k(1\\xrightarrow\u03b12\\xrightarrow\u03b23\\xrightarrow\u03b34)/(\u03b1\u03b2\u03b3),$$":[65],"we":[66],"construct":[67],"$M\\in":[71],"K^b({\\rm":[72],"proj}\u039b)$":[73],"$T=\u03a3\u039b\\in{\\rm":[78],"which":[81],"dim}_k{\\rm":[84],"Hom}_{K^b({\\rm":[85],"proj}B)}\\bigl(\\mathbb{P}_M(T),\u03a3^{-1}\\mathbb{P}_M(T)\\bigr)=1.$$":[86],"Thus":[87],"two-term":[91],"complex":[93],"but":[94],"not":[95],"complex.":[98]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}
