{"id":"https://openalex.org/W7225580239","doi":"https://doi.org/10.5281/zenodo.24054846","title":"Faltings heights of Shimura curve Jacobians at levels divisible by 2 and 3","display_name":"Faltings heights of Shimura curve Jacobians at levels divisible by 2 and 3","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225580239","doi":"https://doi.org/10.5281/zenodo.24054846"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24054846","doi":"https://doi.org/10.5281/zenodo.24054846","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054846","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24054846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116305437","display_name":"Hongmin Li","orcid":"https://orcid.org/0000-0003-0228-0600","observed_orcids":["https://orcid.org/0000-0003-0228-0600"]},"institutions":[{"id":"https://openalex.org/I4400009020","display_name":"Institute of Science Tokyo","ror":"https://ror.org/05dqf9946","country_code":"JP","type":"education","lineage":["https://openalex.org/I4400009020"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Li, Hongmin","raw_affiliation_strings":["Institute of Science Tokyo; The University of Tokyo"],"raw_orcid":"https://orcid.org/0000-0003-0228-0600","affiliations":[{"raw_affiliation_string":"Institute of Science Tokyo; The University of Tokyo","institution_ids":["https://openalex.org/I4400009020","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5116305437"],"corresponding_institution_ids":["https://openalex.org/I4400009020","https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9696999788284302,"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":0.9696999788284302,"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":0.01769999973475933,"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/T11166","display_name":"Analytic Number Theory Research","score":0.006899999920278788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/faltings-height","display_name":"Faltings height","score":0.8899999856948853},{"id":"https://openalex.org/keywords/shimura-curves","display_name":"Shimura curves","score":0.8930000066757202},{"id":"https://openalex.org/keywords/jacobian-matrix","display_name":"Jacobian matrix","score":0.7919999957084656},{"id":"https://openalex.org/keywords/abc-conjecture","display_name":"abc conjecture","score":0.8050000071525574},{"id":"https://openalex.org/keywords/artin-conductor","display_name":"Artin conductor","score":0.8939999938011169},{"id":"https://openalex.org/keywords/normal-model","display_name":"normal model","score":0.328000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.867900013923645},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5508000254631042},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.4528000056743622},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4413999915122986},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.4293000102043152},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.4083999991416931},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4034999907016754},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.39959999918937683},{"id":"https://openalex.org/C188139237","wikidata":"https://www.wikidata.org/wiki/Q50706","display_name":"Square-free integer","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.3637000024318695},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35429999232292175},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.33399999141693115},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.31189998984336853},{"id":"https://openalex.org/C136815107","wikidata":"https://www.wikidata.org/wiki/Q154242","display_name":"Nothing","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C171223647","wikidata":"https://www.wikidata.org/wiki/Q207264","display_name":"Fermat number","level":3,"score":0.2946999967098236},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C2779598827","wikidata":"https://www.wikidata.org/wiki/Q93482","display_name":"Ceylon","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C29641680","wikidata":"https://www.wikidata.org/wiki/Q186875","display_name":"Mersenne prime","level":2,"score":0.27000001072883606}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5281/zenodo.24054846","doi":"https://doi.org/10.5281/zenodo.24054846","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054846","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24054847","doi":"https://doi.org/10.5281/zenodo.24054847","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054847","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24054855","doi":"https://doi.org/10.5281/zenodo.24054855","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054855","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24054861","doi":"https://doi.org/10.5281/zenodo.24054861","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054861","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24054846","doi":"https://doi.org/10.5281/zenodo.24054846","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24054846","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7225588194","https://openalex.org/W2038045793","https://openalex.org/W1989051163","https://openalex.org/W7125377915","https://openalex.org/W2101069578","https://openalex.org/W1994992566","https://openalex.org/W2300100511","https://openalex.org/W4386074661","https://openalex.org/W2462374019","https://openalex.org/W2055210091"],"abstract_inverted_index":{"Let":[0],"$J_0^D(M)$":[1],"be":[2],"the":[3,6,32,50,96,121,144,159,163,167,188,192,204,214,256,262,269],"Jacobian":[4],"of":[5,11,114,166,236,239],"Shimura":[7],"curve":[8],"$X_0^D(M)$,":[9],"$D>1$,":[10],"genus":[12],"$g$,":[13],"and":[14,44,61,68,94,106,130,138,151,162,211,225,272],"$N=DM$.":[15],"The":[16,217],"companion":[17,168],"paper":[18,169,251],"(rStation":[19,249],"math_4)":[20],"proved":[21],"$h_F(J_0^D(M))\\ge(\\frac13-o(1))\\,g\\log":[22],"N$":[23,90],"for":[24,52],"squarefree":[25,60],"$N$":[26],"prime":[27,62,185],"to":[28,39,63,71,171,179],"$6$.":[29],"This":[30],"excludes":[31],"levels":[33],"used":[34],"in":[35,174],"Pasten's":[36,175],"Shimura-curve":[37],"approach":[38],"abc,":[40],"where":[41],"$2^r$":[42],"($r\\le8$)":[43],"$3$":[45,95],"divide":[46,72],"$N$.":[47],"We":[48,200],"remove":[49],"restriction":[51],"bounded":[53,154],"$2$-part:":[54],"if":[55],"$M=M_0":[56],"2^r3^s$":[57],"with":[58,125,183,221,268],"$M_0$":[59],"$6D$,":[64],"$r\\le":[65],"r_0$,":[66],"$s\\le1$,":[67],"$2,3$":[69],"allowed":[70],"$D$":[73],"(including":[74],"$D=6$),":[75],"then":[76],"$12\\,h_F(J/\\mathbf":[77],"Q)\\ge4(g-1)[\\sum_{q\\mid":[78],"D,q\\ge5}\\frac":[79],"q{q-1}\\log":[80],"q+\\sum_{q\\mid":[81],"D,q\\le3}\\frac{3q-1}{4(q-1)}\\log":[82],"q+\\sum_{p\\mid":[83],"M_0}\\frac":[84],"p{p+1}\\log":[85],"p]-C_{r_0}(g+2^{\\omega(N)}\\log":[86],"N)$,":[87],"hence":[88],"$h_F\\ge(\\frac13-o_{r_0}(1))\\,g\\log":[89],"uniformly.":[91],"At":[92],"$2$":[93],"models":[97],"are":[98],"neither":[99],"semistable":[100],"nor":[101],"normal":[102],"after":[103],"base":[104],"change,":[105],"elliptic":[107,131],"sections":[108],"can":[109],"meet":[110],"singular":[111],"points.":[112],"Instead":[113],"computing":[115],"these":[116],"fibres":[117],"we":[118,139],"prove":[119],"that":[120],"completed":[122],"local":[123],"rings,":[124],"group":[126],"action,":[127],"forgetful":[128],"map":[129],"germs,":[132],"have":[133],"finitely":[134],"many":[135,184],"isomorphism":[136],"types,":[137],"use":[140],"three":[141],"sign":[142],"facts:":[143],"Artin":[145],"conductor":[146],"is":[147,153,208,255,264],"non-negative,":[148],"$\\pi^*L\\cdot":[149],"V\\ge0$,":[150],"$V^2$":[152],"below.":[155],"As":[156],"a":[157,231],"consequence,":[158],"lattice":[160],"ceiling":[161],"model-relative":[164],"obstruction":[165],"extend":[170],"all":[172,180],"factorizations":[173],"Theorem":[176],"16.7,":[177],"so":[178],"abc":[181,215],"triples":[182],"factors:":[186],"inside":[187],"stated":[189],"relaxation":[190],"model":[191],"Petersson-ratio":[193],"channel":[194],"has":[195,226],"exponent":[196],"at":[197],"least":[198],"$2/3$.":[199],"claim":[201],"nothing":[202,212],"about":[203,213],"stable":[205],"height,":[206],"which":[207],"left":[209],"open,":[210],"conjecture.":[216],"manuscript":[218,257],"was":[219],"produced":[220],"AI":[222],"research":[223],"agents":[224],"not":[227],"been":[228],"reviewed":[229],"by":[230],"human":[232],"expert.":[233],"Archival":[234],"copy":[235],"version":[237],"1":[238],"this":[240],"paper,":[241],"published":[242,260,270],"on":[243,245],"rStation":[244],"2":[246],"November":[247],"2026":[248],"math":[250],"5,":[252],"v1).":[253],"paper.md":[254,275],"exactly":[258],"as":[259],"there;":[261],"PDF":[263],"typeset":[265],"from":[266],"it":[267],"title":[271],"abstract.":[273],"Files:":[274],"\u2014":[276,280],"SHA-256":[277,281],"0566e63b752cd05142ed33713a4e1f40ad25b180ab9a404f0c663ec0c3cd2ec6":[278],"faltings-heights-of-shimura-curve-jacobians-at-levels-divisible-by-2-and-3.pdf":[279],"bf8aa34577e34744a4205304881a7922362984dcfd8538f85210707a71f31226":[282]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-09T00:00:00"}