{"id":"https://openalex.org/W7223663578","doi":"https://doi.org/10.48550/arxiv.2610.32577","title":"Noetherian local rings without perfectoid towers","display_name":"Noetherian local rings without perfectoid towers","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223663578","doi":"https://doi.org/10.48550/arxiv.2610.32577"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32577","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32577","pdf_url":"https://arxiv.org/pdf/2610.32577","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/2610.32577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054354377","display_name":"Tatsuki Yamaguchi","orcid":"https://orcid.org/0000-0002-6289-9803","observed_orcids":["https://orcid.org/0000-0002-6289-9803"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yamaguchi, Tatsuki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5054354377"],"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.551800012588501,"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"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.551800012588501,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.3978999853134155,"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":0.02419999986886978,"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/perfectoid-rings","display_name":"perfectoid rings","score":0.8939999938011169},{"id":"https://openalex.org/keywords/noetherian-local-rings","display_name":"Noetherian local rings","score":0.8790000081062317},{"id":"https://openalex.org/keywords/perfect-fields","display_name":"perfect fields","score":0.6629999876022339},{"id":"https://openalex.org/keywords/witt-vectors","display_name":"Witt vectors","score":0.414000004529953},{"id":"https://openalex.org/keywords/homogeneous-equations","display_name":"homogeneous equations","score":0.5070000290870667},{"id":"https://openalex.org/keywords/positive-characteristic","display_name":"positive characteristic","score":0.4959999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7950000166893005},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.5609999895095825},{"id":"https://openalex.org/C2779057376","wikidata":"https://www.wikidata.org/wiki/Q3342676","display_name":"Noetherian","level":3,"score":0.535099983215332},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5273000001907349},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5023999810218811},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.49230000376701355},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.41690000891685486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3880999982357025},{"id":"https://openalex.org/C142109727","wikidata":"https://www.wikidata.org/wiki/Q1142704","display_name":"Local ring","level":3,"score":0.3808000087738037},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34049999713897705},{"id":"https://openalex.org/C125225535","wikidata":"https://www.wikidata.org/wiki/Q7049224","display_name":"Noncommutative ring","level":3,"score":0.33980000019073486},{"id":"https://openalex.org/C2777726979","wikidata":"https://www.wikidata.org/wiki/Q582271","display_name":"Noetherian ring","level":3,"score":0.32679998874664307},{"id":"https://openalex.org/C149774684","wikidata":"https://www.wikidata.org/wiki/Q713084","display_name":"Artinian ring","level":4,"score":0.29899999499320984},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.27250000834465027},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C196434610","wikidata":"https://www.wikidata.org/wiki/Q1208658","display_name":"Ring theory","level":4,"score":0.25429999828338623},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.25270000100135803}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.32577","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32577","pdf_url":"https://arxiv.org/pdf/2610.32577","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.2610.32577","doi":"https://doi.org/10.48550/arxiv.2610.32577","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32577","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:2610.32577","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32577","pdf_url":"https://arxiv.org/pdf/2610.32577","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223663578.pdf","grobid_xml":"https://content.openalex.org/works/W7223663578.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4415055985","https://openalex.org/W7162513312","https://openalex.org/W7221834826"],"related_works":["https://openalex.org/W7162513312","https://openalex.org/W7162540610","https://openalex.org/W4403786764","https://openalex.org/W4415360077","https://openalex.org/W7163647143","https://openalex.org/W7016786889","https://openalex.org/W7162590423","https://openalex.org/W3034392010","https://openalex.org/W4415055985","https://openalex.org/W4380608787"],"abstract_inverted_index":{"Let":[0],"$k$":[1],"be":[2],"a":[3,13,24],"perfect":[4],"field":[5],"of":[6],"characteristic":[7],"$p>0$.":[8],"We":[9,36],"prove":[10],"that":[11],"if":[12],"$p$-torsionfree":[14],"ring":[15],"$R$,":[16],"defined":[17],"by":[18],"homogeneous":[19],"equations":[20],"over":[21],"$W(k)$,":[22],"admits":[23],"perfectoid":[25],"tower":[26],"arising":[27],"from":[28],"$(R,(p))$,":[29],"then":[30],"its":[31],"special":[32,49],"fiber":[33],"is":[34],"$F$-liftable.":[35],"also":[37],"give":[38],"explicit":[39],"examples":[40,46],"admitting":[41],"no":[42],"such":[43],"tower,":[44],"including":[45],"with":[47],"$F$-liftable":[48],"fibers.":[50]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-27T00:00:00"}
