{"id":"https://openalex.org/W7223058441","doi":"https://doi.org/10.48550/arxiv.2610.24986","title":"The section conjecture for generic pointed curves","display_name":"The section conjecture for generic pointed curves","publication_year":2026,"publication_date":"2026-10-18","ids":{"openalex":"https://openalex.org/W7223058441","doi":"https://doi.org/10.48550/arxiv.2610.24986"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.24986","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24986","pdf_url":"https://arxiv.org/pdf/2610.24986","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/2610.24986","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159114430","display_name":"Ma Luo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Luo, Ma","raw_affiliation_strings":["Key Laboratory of PMMP , East China Normal University , Shanghai , China","School of Mathematical Sciences , Key Laboratory of MEA (Ministry of Education) , Shanghai"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Key Laboratory of PMMP , East China Normal University , Shanghai , China","institution_ids":["https://openalex.org/I66867065"]},{"raw_affiliation_string":"School of Mathematical Sciences , Key Laboratory of MEA (Ministry of Education) , Shanghai","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079720510","display_name":"Tatsunari Watanabe","orcid":"https://orcid.org/0000-0002-4945-9352","observed_orcids":["https://orcid.org/0000-0002-4945-9352"]},"institutions":[{"id":"https://openalex.org/I4405255987","display_name":"Embry-Riddle Aeronautical University Prescott Arizona Campus","ror":"https://ror.org/03mt1jy53","country_code":"US","type":"education","lineage":["https://openalex.org/I4405255987"]},{"id":"https://openalex.org/I84475105","display_name":"Embry\u2013Riddle Aeronautical University","ror":"https://ror.org/010jskt71","country_code":"US","type":"education","lineage":["https://openalex.org/I84475105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Watanabe, Tatsunari","raw_affiliation_strings":["Mathematics Department , Embry-Riddle Aeronautical University , Prescott , Arizona , USA","School of Mathematical Sciences , Key Laboratory of MEA (Ministry of Education) , Shanghai"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department , Embry-Riddle Aeronautical University , Prescott , Arizona , USA","institution_ids":["https://openalex.org/I4405255987","https://openalex.org/I84475105"]},{"raw_affiliation_string":"School of Mathematical Sciences , Key Laboratory of MEA (Ministry of Education) , Shanghai","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9146000146865845,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9146000146865845,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.08250000327825546,"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":0.000699999975040555,"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/section-conjecture","display_name":"section conjecture","score":0.9440000057220459},{"id":"https://openalex.org/keywords/arithmetic-fundamental-group","display_name":"arithmetic fundamental group","score":0.8920000195503235},{"id":"https://openalex.org/keywords/rational-points","display_name":"rational points","score":0.6669999957084656},{"id":"https://openalex.org/keywords/non-abelian-cohomology","display_name":"non-abelian cohomology","score":0.9879999756813049},{"id":"https://openalex.org/keywords/hyperelliptic-curves","display_name":"hyperelliptic curves","score":0.8949999809265137},{"id":"https://openalex.org/keywords/configuration-space","display_name":"configuration space","score":0.6629999876022339},{"id":"https://openalex.org/keywords/finitely-generated-fields","display_name":"finitely generated fields","score":0.8859999775886536}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8385999798774719},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.7407000064849854},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6916000247001648},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5817999839782715},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.578499972820282},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.5525000095367432},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.5419999957084656},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C3387666","wikidata":"https://www.wikidata.org/wiki/Q6889798","display_name":"Moduli of algebraic curves","level":3,"score":0.38179999589920044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38019999861717224},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.3646000027656555},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3125},{"id":"https://openalex.org/C162860070","wikidata":"https://www.wikidata.org/wiki/Q142140","display_name":"Finitely-generated abelian group","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.2703999876976013},{"id":"https://openalex.org/C205633959","wikidata":"https://www.wikidata.org/wiki/Q2494915","display_name":"Unipotent","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2612000107765198},{"id":"https://openalex.org/C156330621","wikidata":"https://www.wikidata.org/wiki/Q3393476","display_name":"Rational point","level":3,"score":0.25929999351501465}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.24986","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24986","pdf_url":"https://arxiv.org/pdf/2610.24986","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.2610.24986","doi":"https://doi.org/10.48550/arxiv.2610.24986","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.24986","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:2610.24986","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.24986","pdf_url":"https://arxiv.org/pdf/2610.24986","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/G1609915050","display_name":null,"funder_award_id":"22DZ2229014","funder_id":"https://openalex.org/F4320321885","funder_display_name":"Science and Technology Commission of Shanghai Municipality"}],"funders":[{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223058441.pdf","grobid_xml":"https://content.openalex.org/works/W7223058441.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1853729283","https://openalex.org/W2011392880","https://openalex.org/W2014248358","https://openalex.org/W2039225816","https://openalex.org/W2062609527","https://openalex.org/W2078326108","https://openalex.org/W2078892083","https://openalex.org/W2086624417","https://openalex.org/W2090300239","https://openalex.org/W2104604380","https://openalex.org/W2504834220","https://openalex.org/W2963752263","https://openalex.org/W2963849315","https://openalex.org/W2963969370","https://openalex.org/W4407806644","https://openalex.org/W4413270961"],"related_works":["https://openalex.org/W2963969370","https://openalex.org/W3092687538","https://openalex.org/W4377009833","https://openalex.org/W1741954134","https://openalex.org/W2504834220","https://openalex.org/W7155516845","https://openalex.org/W2963752263","https://openalex.org/W2982834771","https://openalex.org/W2183770603","https://openalex.org/W6995615482"],"abstract_inverted_index":{"Let":[0],"$k/\\mathbb":[1],"Q$":[2,107],"be":[3,14],"finitely":[4,103],"generated,":[5],"let":[6,11],"$g\\geq3$":[7],"and":[8,10,49,129,145,158,168],"$n\\geq1$,":[9],"$\\mathcal":[12],"M_{g,n/k}$":[13],"the":[15,37,46,53,57,62,72,94,118,138,164,172,176],"moduli":[16,47,177],"stack":[17,48,178],"of":[18,56,61,93,113],"smooth":[19],"proper":[20],"genus-$g$":[21,40],"curves":[22],"with":[23,90,108,133,179],"$n$":[24,73],"distinct":[25],"ordered":[26],"markings.":[27],"Put":[28],"$K=k(\\mathcal":[29],"M_{g,n/k})$.":[30],"We":[31],"prove":[32],"Grothendieck's":[33],"section":[34,120,173],"conjecture":[35,121],"for":[36,80,85,116],"generic":[38,169],"$n$-pointed":[39],"curve":[41,65],"over":[42,101,105,175,181],"$K$.":[43,182],"Over":[44],"both":[45],"its":[50],"function":[51],"field,":[52],"continuous":[54],"sections":[55,151],"arithmetic":[58],"fundamental-group":[59],"extension":[60],"universal":[63],"complete":[64],"are,":[66],"up":[67],"to":[68,152],"geometric":[69],"conjugacy,":[70],"exactly":[71],"tautological":[74],"sections.":[75,155],"The":[76,123],"same":[77],"classification":[78],"holds":[79],"every":[81,86],"geometrically":[82,153],"pro-$\\ell$":[83,154],"quotient,":[84],"prime":[87],"$\\ell$.":[88],"Together":[89],"Hain's":[91,127],"determination":[92],"rational":[95,114],"points,":[96],"these":[97],"classifications":[98],"give":[99],"examples":[100],"fields":[102],"generated":[104],"$\\mathbb":[106],"any":[109],"prescribed":[110],"positive":[111],"number":[112],"points":[115],"which":[117],"full":[119,165],"holds.":[122],"proof":[124],"builds":[125],"on":[126],"weighted-completion":[128],"nonabelian":[130],"cohomology":[131],"methods,":[132],"a":[134],"hyperelliptic":[135],"calculation":[136],"providing":[137],"genus-three":[139],"input.":[140],"An":[141],"integral":[142],"normalizer":[143],"lemma":[144],"moving-mark":[146],"arguments":[147],"pass":[148],"from":[149],"unipotent":[150],"Configuration":[156],"spaces":[157],"Mochizuki's":[159],"open":[160],"Hom":[161],"theorem":[162],"yield":[163],"profinite":[166],"classification,":[167],"descent":[170],"identifies":[171],"classes":[174],"those":[180]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}
