{"id":"https://openalex.org/W7220935312","doi":"https://doi.org/10.48550/arxiv.2610.09319","title":"Derived Picard reconstruction for graded surfaces with stops","display_name":"Derived Picard reconstruction for graded surfaces with stops","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220935312","doi":"https://doi.org/10.48550/arxiv.2610.09319"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09319","pdf_url":"https://arxiv.org/pdf/2610.09319","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/2610.09319","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5115560822","display_name":"Wen Chang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Wen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109651718","display_name":"Dongjian Wu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Dongjian","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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9726999998092651,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9726999998092651,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.007000000216066837,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.006899999920278788,"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/mapping-class-group","display_name":"mapping class group","score":0.7829999923706055},{"id":"https://openalex.org/keywords/serre-functor","display_name":"Serre functor","score":0.9409999847412109},{"id":"https://openalex.org/keywords/line-fields","display_name":"line fields","score":0.7279999852180481},{"id":"https://openalex.org/keywords/higher-genus-surfaces","display_name":"higher genus surfaces","score":0.5270000100135803},{"id":"https://openalex.org/keywords/boundary-components","display_name":"boundary components","score":0.609000027179718}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8842999935150146},{"id":"https://openalex.org/C2777283802","wikidata":"https://www.wikidata.org/wiki/Q2042963","display_name":"Picard group","level":3,"score":0.7103000283241272},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.5791000127792358},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5674999952316284},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5364999771118164},{"id":"https://openalex.org/C196278274","wikidata":"https://www.wikidata.org/wiki/Q3845212","display_name":"Mapping class group","level":3,"score":0.5245000123977661},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46970000863075256},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3425000011920929},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.33079999685287476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3075999915599823},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28619998693466187},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.27630001306533813},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09319","pdf_url":"https://arxiv.org/pdf/2610.09319","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.2610.09319","doi":"https://doi.org/10.48550/arxiv.2610.09319","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09319","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:2610.09319","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09319","pdf_url":"https://arxiv.org/pdf/2610.09319","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/G8090935680","display_name":null,"funder_award_id":"12271321","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220935312.pdf","grobid_xml":"https://content.openalex.org/works/W7220935312.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2785626087","https://openalex.org/W2937990504","https://openalex.org/W4361865971","https://openalex.org/W4415241199","https://openalex.org/W4417104274"],"related_works":["https://openalex.org/W7214977279","https://openalex.org/W4417104274","https://openalex.org/W2012003321","https://openalex.org/W7100256804","https://openalex.org/W1547224787","https://openalex.org/W1986062607","https://openalex.org/W7152514369","https://openalex.org/W2924738217","https://openalex.org/W4293093437","https://openalex.org/W7097561953"],"abstract_inverted_index":{"We":[0,77],"study":[1],"reconstruction":[2],"of":[3,19,84,140],"graded":[4,56,149],"surfaces":[5],"with":[6,41,49,64,88,113,134,151],"stops":[7,42,114,152],"$(S,M,\u03b7)$":[8,153],"from":[9],"their":[10,20],"mapping":[11,35],"class":[12,36],"groups":[13,18],"and":[14,68,92,171],"the":[15,33,39,45,50,54,60,66,69,89,106,111,128,135,148],"derived":[16,46,61,131],"Picard":[17,47,62,132],"partially":[21],"wrapped":[22],"Fukaya":[23],"categories.":[24],"In":[25],"genus":[26,124],"at":[27,125,142,159],"least":[28,126,160],"two,":[29,127,169],"we":[30,103],"prove":[31],"that":[32,105],"ungraded":[34],"group":[37,48,63],"determines":[38,53,110,147],"surface":[40,57,112,150],"$(S,M)$,":[43],"while":[44,164],"shift":[51,67,136],"distinguished":[52,72],"underlying":[55],"$(S,\u03b7)$.":[58],"Nevertheless,":[59],"both":[65],"Serre":[70,108],"functor":[71],"has":[73,138,156],"countably":[74],"infinite":[75],"fibres.":[76],"also":[78],"construct":[79],"arbitrarily":[80],"large":[81],"finite":[82],"families":[83],"pairwise":[85],"non-equivalent":[86],"categories":[87],"same":[90],"invariant":[91],"Grothendieck":[93],"rank.":[94],"For":[95,119],"line":[96,121],"fields":[97,122],"induced":[98],"by":[99],"nowhere-vanishing":[100],"vector":[101],"fields,":[102],"show":[104],"rational":[107],"representation":[109],"$(S,M)$":[115],"in":[116,123],"every":[117],"genus.":[118],"arbitrary":[120],"full":[129],"integral":[130],"representation,":[133],"distinguished,":[137],"fibres":[139,166],"cardinality":[141],"most":[143],"four.":[144],"It":[145],"completely":[146],"when":[154],"$S$":[155],"one":[157],"or":[158],"five":[161],"boundary":[162,173],"components,":[163],"non-singleton":[165],"occur":[167],"for":[168],"three,":[170],"four":[172],"components.":[174]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}