{"id":"https://openalex.org/W7203877126","doi":"https://doi.org/10.48550/arxiv.2608.19921","title":"Recollements of derived categories from $n$-term big tilting complexes","display_name":"Recollements of derived categories from $n$-term big tilting complexes","publication_year":2026,"publication_date":"2026-08-20","ids":{"openalex":"https://openalex.org/W7203877126","doi":"https://doi.org/10.48550/arxiv.2608.19921"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.19921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19921","pdf_url":"https://arxiv.org/pdf/2608.19921","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/2608.19921","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138107467","display_name":"Shengyong Pan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pan, Shengyong","raw_affiliation_strings":[". School of Mathematics and Statistics , Beijing Jiaotong University , 100044 Beijing , China Beijing Key Laboratory of Biological Big Data and Topological Statistics ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Mathematics and Statistics , Beijing Jiaotong University , 100044 Beijing , China Beijing Key Laboratory of Biological Big Data and Topological Statistics ,","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147774011","display_name":"Huabo Xu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]},{"id":"https://openalex.org/I62853816","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855","country_code":"CN","type":"education","lineage":["https://openalex.org/I62853816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu, Huabo","raw_affiliation_strings":[". School of Science , Beijing University of Civil Engineering and Architecture , 102616 Beijing , China","Beijing Jiaotong University , 100044 Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":". School of Science , Beijing University of Civil Engineering and Architecture , 102616 Beijing , China","institution_ids":["https://openalex.org/I62853816"]},{"raw_affiliation_string":"Beijing Jiaotong University , 100044 Beijing , China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.9961000084877014,"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":0.9961000084877014,"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":0.0010999999940395355,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/recollements","display_name":"recollements","score":0.8769999742507935},{"id":"https://openalex.org/keywords/derived-categories","display_name":"derived categories","score":0.9440000057220459},{"id":"https://openalex.org/keywords/endomorphism-rings","display_name":"endomorphism rings","score":0.7490000128746033},{"id":"https://openalex.org/keywords/jacobson-radical","display_name":"Jacobson radical","score":0.6949999928474426},{"id":"https://openalex.org/keywords/derived-equivalence","display_name":"derived equivalence","score":0.5799999833106995}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8075000047683716},{"id":"https://openalex.org/C2780617661","wikidata":"https://www.wikidata.org/wiki/Q541563","display_name":"Subcategory","level":2,"score":0.6748999953269958},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.5414999723434448},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5389000177383423},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.531499981880188},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5288000106811523},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5030999779701233},{"id":"https://openalex.org/C186921422","wikidata":"https://www.wikidata.org/wiki/Q318737","display_name":"Abelian category","level":3,"score":0.4641000032424927},{"id":"https://openalex.org/C143161588","wikidata":"https://www.wikidata.org/wiki/Q906907","display_name":"Coherent sheaf","level":2,"score":0.41679999232292175},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.3903999924659729},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.3772999942302704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3634999990463257},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3327000141143799},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.32269999384880066},{"id":"https://openalex.org/C18116961","wikidata":"https://www.wikidata.org/wiki/Q734209","display_name":"Generating set of a group","level":2,"score":0.31690001487731934},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.29170000553131104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27950000762939453},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.26499998569488525},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.25279998779296875}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.19921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19921","pdf_url":"https://arxiv.org/pdf/2608.19921","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.2608.19921","doi":"https://doi.org/10.48550/arxiv.2608.19921","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.19921","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:2608.19921","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.19921","pdf_url":"https://arxiv.org/pdf/2608.19921","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":[{"id":"https://openalex.org/F4320325174","display_name":"Beijing University of Civil Engineering and Architecture","ror":"https://ror.org/02yj0p855"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7203877126.pdf","grobid_xml":"https://content.openalex.org/works/W7203877126.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391927563","https://openalex.org/W3103103969","https://openalex.org/W6928960273","https://openalex.org/W2078962382","https://openalex.org/W3126947502","https://openalex.org/W1691519315","https://openalex.org/W2153714028","https://openalex.org/W3169350191","https://openalex.org/W2026508146","https://openalex.org/W2153728975"],"abstract_inverted_index":{"Let":[0],"$A$":[1],"be":[2,8,204],"a":[3,9,18,63,73,78,118],"ring,":[4],"let":[5],"${\\bf":[6,24,39],"T}$":[7],"finite-term":[10],"big":[11,154],"tilting":[12,155],"complex":[13],"over":[14,189],"$A$,":[15],"and":[16,68,93,202],"choose":[17],"bounded":[19],"projective":[20,101,180],"representative":[21],"$\\cpx{P}$":[22],"of":[23,33,81,103,176],"T}$.":[25],"Put":[26],"$B=\\End_{\\D{A}}(\\cpx{P})$.":[27],"We":[28,109],"prove":[29],"that":[30],"the":[31,34,44,56,82,100,104,113,135,140,149,161,168],"kernel":[32,83,114],"associated":[35],"derived":[36,45,209],"tensor":[37],"functor":[38],"R}:\\D{B}\\to\\D{A}$":[40],"is":[41,91,97,115,128,163],"equivalent,":[42],"through":[43],"inclusion,":[46],"to":[47,139],"$\\D{\\mathscr":[48,66],"E}$,":[49],"where":[50],"$\\mathscr":[51,89,126],"E=\\Ker({\\bf":[52],"R})\\cap":[53],"B\\Modcat$":[54],"carries":[55],"inherited":[57],"exact":[58,200],"structure.":[59],"Consequently,":[60],"$\\D{B}$":[61],"admits":[62],"recollement":[64],"by":[65,117,165,208],"E}$":[67],"$\\D{A}$.":[69],"The":[70,87],"proof":[71],"combines":[72],"dg":[74],"double-centralizer":[75],"argument":[76],"with":[77],"functorial":[79],"realisation":[80],"on":[84],"unbounded":[85],"complexes.":[86,156],"category":[88],"E$":[90,127],"definable":[92],"$d$-symmetric":[94],"whenever":[95],"$d$":[96],"at":[98,144],"least":[99],"amplitude":[102,143,162],"underlying":[105],"perfect":[106],"right":[107],"$B$-complex.":[108],"also":[110],"characterise":[111],"when":[112,125,134],"induced":[116],"homological":[119],"ring":[120],"epimorphism:":[121],"this":[122,147],"holds":[123],"precisely":[124],"an":[129],"abelian":[130],"subcategory,":[131],"or":[132],"equivalently":[133],"standard":[136],"$t$-structure":[137],"restricts":[138],"kernel.":[141],"In":[142],"most":[145],"one,":[146],"recovers":[148],"universal-localisation":[150],"description":[151],"for":[152],"two-term":[153],"Over":[157],"semiperfect":[158],"endomorphism":[159],"rings,":[160],"detected":[164],"reduction":[166],"modulo":[167],"Jacobson":[169],"radical.":[170],"Finally,":[171],"we":[172],"construct":[173],"non-compact":[174],"examples":[175],"arbitrarily":[177],"large":[178],"minimal":[179],"amplitude.":[181],"One":[182],"family":[183],"yields":[184],"algebraic":[185],"Calkin":[186],"quotients;":[187],"another,":[188],"connected":[190],"rings":[191],"constructed":[192],"from":[193,206],"singular":[194],"local":[195],"hypersurfaces,":[196],"has":[197],"nonzero,":[198],"non-abelian":[199],"kernels":[201],"cannot":[203],"obtained":[205],"modules":[207],"equivalences":[210],"between":[211],"ordinary":[212],"rings.":[213]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-22T00:00:00"}
