{"id":"https://openalex.org/W7214908565","doi":"https://doi.org/10.48550/arxiv.2610.37075","title":"All Strict Calabi--Yau Threefolds of Height One Lift to Characteristic 0","display_name":"All Strict Calabi--Yau Threefolds of Height One Lift to Characteristic 0","publication_year":2026,"publication_date":"2026-09-30","ids":{"openalex":"https://openalex.org/W7214908565","doi":"https://doi.org/10.48550/arxiv.2610.37075"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.37075","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37075","pdf_url":"https://arxiv.org/pdf/2610.37075","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.37075","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069809843","display_name":"Matthew Ward","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ward, Matthew","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5069809843"],"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":0.9984999895095825,"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/T10061","display_name":"Algebraic Geometry and Number Theory","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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0005000000237487257,"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/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/lifting-to-characteristic-zero","display_name":"lifting to characteristic zero","score":0.8479999899864197},{"id":"https://openalex.org/keywords/bockstein-homomorphism","display_name":"Bockstein homomorphism","score":0.8040000200271606},{"id":"https://openalex.org/keywords/crystalline-cohomology","display_name":"crystalline cohomology","score":0.7710000276565552},{"id":"https://openalex.org/keywords/p-adic-hodge-theory","display_name":"p-adic Hodge theory","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.8148999810218811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7620000243186951},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.7243000268936157},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5394999980926514},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.4650999903678894},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.3977000117301941},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3921999931335449},{"id":"https://openalex.org/C80551277","wikidata":"https://www.wikidata.org/wiki/Q11210","display_name":"Coordinate system","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34439998865127563},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32429999113082886},{"id":"https://openalex.org/C204366326","wikidata":"https://www.wikidata.org/wiki/Q3027650","display_name":"Deformation (meteorology)","level":2,"score":0.28189998865127563}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.37075","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37075","pdf_url":"https://arxiv.org/pdf/2610.37075","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.2610.37075","doi":"https://doi.org/10.48550/arxiv.2610.37075","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.37075","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"},{"id":"doi:10.5281/zenodo.23061935","doi":"https://doi.org/10.5281/zenodo.23061935","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23061935","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.23061936","doi":"https://doi.org/10.5281/zenodo.23061936","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23061936","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":"pmh:oai:arXiv.org:2610.37075","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.37075","pdf_url":"https://arxiv.org/pdf/2610.37075","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214908565.pdf","grobid_xml":"https://content.openalex.org/works/W7214908565.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1972675952","https://openalex.org/W2580312724","https://openalex.org/W2950354993","https://openalex.org/W4400668366","https://openalex.org/W1966821868","https://openalex.org/W2592229075","https://openalex.org/W2607937709","https://openalex.org/W3087150481","https://openalex.org/W757342460","https://openalex.org/W2953389670"],"abstract_inverted_index":{"We":[0],"prove":[1],"that":[2,52,73],"every":[3],"strict":[4],"Calabi--Yau":[5,96],"threefold":[6,97],"of":[7,17,46,64,68,98,122],"Artin--Mazur":[8],"height":[9,99],"one":[10,100],"over":[11,59,111,116],"an":[12],"algebraically":[13],"closed":[14],"field":[15],"k":[16],"characteristic":[18,107],"p>0":[19],"admits":[20],"a":[21,57,65,95,120],"projective":[22],"lift":[23,58],"to":[24,55,80],"W(k).":[25],"No":[26],"assumption":[27],"is":[28,39,61],"made":[29,79],"on":[30],"the":[31,42,53,62,84],"torsion":[32,66],"in":[33,106],"its":[34,69],"crystalline":[35,43],"cohomology,":[36],"and":[37,48,72,104,124],"p":[38],"arbitrary.":[40],"Using":[41],"period":[44,70],"map":[45],"Brantner":[47],"Taelman,":[49],"we":[50],"show":[51],"obstruction":[54],"extending":[56],"W_n(k)":[60],"Bockstein":[63],"coordinate":[67,75],"point,":[71],"this":[74],"can":[76],"always":[77],"be":[78,92],"vanish":[81],"by":[82,102],"varying":[83],"lift.":[85],"The":[86],"mixed-characteristic":[87],"deformation":[88],"functor":[89],"need":[90],"not":[91,114],"smooth:":[93],"for":[94],"constructed":[101],"Addington":[103],"Bragg":[105],"3,":[108],"some":[109],"lifts":[110],"W_2(k)":[112],"do":[113],"extend":[115],"W_3(k).":[117],"This":[118],"disproves":[119],"conjecture":[121],"Achinger":[123],"Zdanowicz.":[125]},"counts_by_year":[],"updated_date":"2026-10-31T12:09:11.096373","created_date":"2026-10-01T00:00:00"}