{"id":"https://openalex.org/W7223109188","doi":"https://doi.org/10.48550/arxiv.2610.28149","title":"The stacky approach to de Rham-Witt cohomology","display_name":"The stacky approach to de Rham-Witt cohomology","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223109188","doi":"https://doi.org/10.48550/arxiv.2610.28149"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.28149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28149","pdf_url":"https://arxiv.org/pdf/2610.28149","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/2610.28149","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008256268","display_name":"Yuanning Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zhang, Yuanning","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5008256268"],"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.8701000213623047,"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":0.8701000213623047,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.11720000207424164,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.0017000000225380063,"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/stable-infinity-categories","display_name":"stable infinity-categories","score":0.6620000004768372},{"id":"https://openalex.org/keywords/poincare-duality","display_name":"Poincar\u00e9 duality","score":0.7689999938011169},{"id":"https://openalex.org/keywords/kunneth-formula","display_name":"K\u00fcnneth formula","score":0.9919999837875366},{"id":"https://openalex.org/keywords/frobenius","display_name":"Frobenius","score":0.5320000052452087},{"id":"https://openalex.org/keywords/perfect-fields-of-positive-characteristic","display_name":"perfect fields of positive characteristic","score":0.7229999899864197},{"id":"https://openalex.org/keywords/triangulated-categories","display_name":"triangulated categories","score":0.4950000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8762000203132629},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6707000136375427},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5238999724388123},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4675000011920929},{"id":"https://openalex.org/C2780212368","wikidata":"https://www.wikidata.org/wiki/Q7840150","display_name":"Triangulated category","level":4,"score":0.4496000111103058},{"id":"https://openalex.org/C195800304","wikidata":"https://www.wikidata.org/wiki/Q7601281","display_name":"Star product","level":2,"score":0.4027999937534332},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3828999996185303},{"id":"https://openalex.org/C2779185822","wikidata":"https://www.wikidata.org/wiki/Q5141399","display_name":"Cohomology ring","level":4,"score":0.3727000057697296},{"id":"https://openalex.org/C128489963","wikidata":"https://www.wikidata.org/wiki/Q1187724","display_name":"Filtration (mathematics)","level":2,"score":0.3695000112056732},{"id":"https://openalex.org/C9395851","wikidata":"https://www.wikidata.org/wiki/Q177929","display_name":"Stack (abstract data type)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.31029999256134033},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C11846945","wikidata":"https://www.wikidata.org/wiki/Q1082992","display_name":"Equivalence of categories","level":3,"score":0.28299999237060547},{"id":"https://openalex.org/C109593458","wikidata":"https://www.wikidata.org/wiki/Q5262626","display_name":"Derived category","level":3,"score":0.28290000557899475},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C126867241","wikidata":"https://www.wikidata.org/wiki/Q3388699","display_name":"Cup product","level":5,"score":0.26100000739097595},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2556000053882599},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.28149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28149","pdf_url":"https://arxiv.org/pdf/2610.28149","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.2610.28149","doi":"https://doi.org/10.48550/arxiv.2610.28149","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.28149","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:2610.28149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.28149","pdf_url":"https://arxiv.org/pdf/2610.28149","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/W7223109188.pdf","grobid_xml":"https://content.openalex.org/works/W7223109188.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W3039213385","https://openalex.org/W3197337335","https://openalex.org/W4226310301","https://openalex.org/W4283393961","https://openalex.org/W4405033259","https://openalex.org/W4406272387","https://openalex.org/W4415279616","https://openalex.org/W4416528685","https://openalex.org/W7150936207","https://openalex.org/W7171767127","https://openalex.org/W7212290908","https://openalex.org/W7214224007","https://openalex.org/W7215057793"],"related_works":["https://openalex.org/W2134872946","https://openalex.org/W82392920","https://openalex.org/W2949538451","https://openalex.org/W2803203383","https://openalex.org/W2502578622","https://openalex.org/W7100032156","https://openalex.org/W4392488726","https://openalex.org/W2516013171","https://openalex.org/W3009108960","https://openalex.org/W4414744686"],"abstract_inverted_index":{"Let":[0],"$k$":[1],"be":[2],"a":[3,30,43,141,162],"perfect":[4,51],"field":[5],"of":[6,13,26,34,47,84,86,143,153,168,201,204],"characteristic":[7],"$p>0$.":[8],"Ekedahl":[9],"proved":[10],"an":[11,80],"equivalence":[12,46],"triangulated":[14],"categories":[15],"between":[16,50,122],"bounded":[17,54],"coherent":[18,55],"complexes":[19,25,56],"over":[20,57,206],"the":[21,38,58,96,100,103,109,112,123,129,135,151,159,166,169,198],"Raynaud":[22,59],"ring":[23,60],"and":[24,53,89,94,102,128,147,158,165,182,195,203],"$F$-gauges.":[27],"We":[28],"give":[29],"geometric":[31],"proof,":[32,36],"independent":[33],"his":[35],"that":[37,197],"de":[39,186],"Rham-Witt":[40,187],"realization":[41],"is":[42,79,140],"symmetric":[44],"monoidal":[45],"stable":[48],"$\\infty$-categories":[49],"$F$-gauges":[52],"with":[61],"Ekedahl's":[62,179],"completed":[63],"star":[64,170],"product,":[65],"as":[66,161],"expected":[67],"by":[68],"Illusie.":[69],"The":[70],"geometry":[71],"comes":[72],"from":[73,108,150,156,189],"topological":[74],"restriction":[75,146],"homology:":[76],"$\\mathrm{TR}^r(k;\\mathbf":[77],"Z_p)^{hS^1}$":[78],"iterated":[81],"fibre":[82,97],"product":[83,98,171],"copies":[85],"$\\mathrm{TC}^-(k;\\mathbf":[87],"Z_p)$,":[88],"taking":[90],"even":[91],"stacks":[92],"before":[93],"after":[95],"gives":[99],"genuine":[101,110,136],"naive":[104,113],"$r$-Nygaard":[105,114,118,137],"stacks.":[106],"Pushforward":[107],"to":[111],"stack":[115],"realizes":[116],"Andriopoulos'":[117],"filtrations,":[119],"which":[120,139],"interpolate":[121],"Nygaard":[124,144],"filtration":[125,131],"at":[126,132],"$r=1$":[127],"Hodge-Witt":[130],"$r=\\infty$.":[133],"On":[134],"stack,":[138],"chain":[142],"charts,":[145],"Frobenius":[148],"come":[149],"inclusions":[152],"sub-chains,":[154],"Verschiebung":[155],"duality,":[157],"differential":[160],"Bockstein":[163],"operator,":[164],"relations":[167],"become":[172],"projection":[173],"formulas.":[174],"As":[175],"applications,":[176],"we":[177],"deduce":[178],"K\u00fcnneth":[180],"formula":[181],"Poincar\u00e9":[183],"duality":[184],"for":[185,192],"cohomology":[188],"their":[190],"counterparts":[191],"$F$-gauge":[193],"cohomology,":[194],"show":[196],"special-value":[199],"formulas":[200],"Illusie":[202],"Mondal":[205],"finite":[207],"fields":[208],"are":[209],"equivalent.":[210]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}