{"id":"https://openalex.org/W7213335933","doi":"https://doi.org/10.13140/rg.2.2.19944.64009","title":"Continuous Comparison of Free Simplicial Prounipotent and Pro-$p$ Resolutions","display_name":"Continuous Comparison of Free Simplicial Prounipotent and Pro-$p$ Resolutions","publication_year":2026,"publication_date":"2026-09-15","ids":{"openalex":"https://openalex.org/W7213335933","doi":"https://doi.org/10.13140/rg.2.2.19944.64009"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.21513","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21513","pdf_url":"https://arxiv.org/pdf/2609.21513","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/2609.21513","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006920805","display_name":"Andrey Mikhovich","orcid":"https://orcid.org/0000-0002-2025-9154","observed_orcids":["https://orcid.org/0000-0002-2025-9154"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andrey Mikhovich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5006920805"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9897000193595886,"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"}},"topics":[{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9897000193595886,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.0032999999821186066,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.0027000000700354576,"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/pro-p-groups","display_name":"pro-p groups","score":0.9940000176429749},{"id":"https://openalex.org/keywords/comparison-theorems","display_name":"comparison theorems","score":0.8009999990463257},{"id":"https://openalex.org/keywords/free-base","display_name":"free base","score":0.6179999709129333},{"id":"https://openalex.org/keywords/degeneracy","display_name":"degeneracy","score":0.7120000123977661},{"id":"https://openalex.org/keywords/free-pro-p-groups","display_name":"free pro-p groups","score":0.8849999904632568},{"id":"https://openalex.org/keywords/characteristic-zero","display_name":"characteristic zero","score":0.5619999766349792}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5072000026702881},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3774999976158142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31209999322891235},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27790001034736633},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2637999951839447},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2563000023365021},{"id":"https://openalex.org/C2776055716","wikidata":"https://www.wikidata.org/wiki/Q7316893","display_name":"Retract","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.24330000579357147}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.21513","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21513","pdf_url":"https://arxiv.org/pdf/2609.21513","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.2609.21513","doi":"https://doi.org/10.48550/arxiv.2609.21513","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.21513","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:10.13140/rg.2.2.19944.64009","doi":"https://doi.org/10.13140/rg.2.2.19944.64009","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.19944.64009","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.21513","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.21513","pdf_url":"https://arxiv.org/pdf/2609.21513","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/W7213335933.pdf","grobid_xml":"https://content.openalex.org/works/W7213335933.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1853729283","https://openalex.org/W1980234293","https://openalex.org/W2090539484","https://openalex.org/W2316265374","https://openalex.org/W4236256974","https://openalex.org/W4244007815","https://openalex.org/W6884978673"],"related_works":["https://openalex.org/W6884978673","https://openalex.org/W2141547660","https://openalex.org/W2596066802","https://openalex.org/W2526289932","https://openalex.org/W7099937868","https://openalex.org/W1633562557","https://openalex.org/W2028004159","https://openalex.org/W4400094367","https://openalex.org/W2104369783","https://openalex.org/W3173649034"],"abstract_inverted_index":{"We":[0,88],"give":[1],"a":[2,20],"continuous":[3,50],"version":[4],"of":[5,16,22,26,57,72,136],"the":[6,14,45,54,63,69,90,97,110,116,122],"comparison":[7],"theorem":[8],"for":[9],"free":[10,32,59,73,91],"simplicial":[11,83,105],"resolutions":[12,30],"in":[13,96,121,129],"categories":[15],"prounipotent":[17],"groups":[18],"over":[19],"field":[21],"characteristic":[23,43],"zero":[24,44],"and":[25,53,80,112],"pro-$p$":[27,64,74],"groups.":[28,75],"The":[29,125],"carry":[31],"bases":[33,92],"compatible":[34],"with":[35],"degeneracies;":[36],"their":[37],"ranks":[38],"may":[39],"be":[40],"infinite.":[41],"In":[42,62],"lifting":[46,78,123],"step":[47],"follows":[48,67],"from":[49,68,109],"linear":[51],"splittings":[52],"universal":[55],"property":[56],"completed":[58],"Lie":[60],"algebras.":[61],"case":[65],"it":[66],"classical":[70],"projectivity":[71],"A":[76],"relative":[77],"argument":[79],"an":[81],"explicit":[82],"cylinder":[84],"establish":[85],"homotopy":[86],"uniqueness.":[87],"formulate":[89],"using":[93],"actual":[94],"surjections":[95],"simplex":[98],"category,":[99],"so":[100],"degeneracy":[101],"words":[102],"related":[103],"by":[104],"identities":[106],"are":[107],"identified":[108],"outset,":[111],"we":[113],"spell":[114],"out":[115],"full":[117],"matching":[118],"objects":[119],"used":[120],"argument.":[124],"question":[126],"arose":[127],"naturally":[128],"our":[130],"preceding":[131],"work":[132],"on":[133],"Bousfield--Kan":[134],"completions":[135],"subcontractible":[137],"presentations.":[138]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-16T00:00:00"}