{"id":"https://openalex.org/W7214119776","doi":"https://doi.org/10.48550/arxiv.2609.25148","title":"Categorical representations of algebraic groups in positive characteristic","display_name":"Categorical representations of algebraic groups in positive characteristic","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214119776","doi":"https://doi.org/10.48550/arxiv.2609.25148"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.25148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25148","pdf_url":"https://arxiv.org/pdf/2609.25148","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/2609.25148","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083785442","display_name":"Pramod N. Achar","orcid":"https://orcid.org/0000-0002-3447-5165","observed_orcids":["https://orcid.org/0000-0002-3447-5165"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Achar, Pramod N.","raw_affiliation_strings":["UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075018822","display_name":"Gurbir Dhillon","orcid":"https://orcid.org/0000-0002-3894-538X","observed_orcids":["https://orcid.org/0000-0002-3894-538X"]},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]},{"id":"https://openalex.org/I198244214","display_name":"Universit\u00e9 Clermont Auvergne","ror":"https://ror.org/01a8ajp46","country_code":"FR","type":"education","lineage":["https://openalex.org/I198244214"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Dhillon, Gurbir","raw_affiliation_strings":["UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA","Universit\u00e9 Clermont Auvergne , CNRS , LMBP , F-63000 Clermont-Ferrand , France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Universit\u00e9 Clermont Auvergne , CNRS , LMBP , F-63000 Clermont-Ferrand , France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I198244214"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005759805","display_name":"Simon Riche","orcid":"https://orcid.org/0000-0002-8697-0854","observed_orcids":["https://orcid.org/0000-0002-8697-0854"]},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Riche, Simon","raw_affiliation_strings":["UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UCLA Mathematics Department , Los Angeles , CA 90095-1555 , USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7964000105857849,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.7964000105857849,"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":0.17110000550746918,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.021199999377131462,"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/affine-group-schemes","display_name":"affine group schemes","score":0.7960000038146973},{"id":"https://openalex.org/keywords/positive-characteristic","display_name":"positive characteristic","score":0.9089999794960022},{"id":"https://openalex.org/keywords/harish-chandra-bimodules","display_name":"Harish-Chandra bimodules","score":0.7940000295639038},{"id":"https://openalex.org/keywords/frobenius-morphism","display_name":"Frobenius endomorphism","score":0.8460000157356262},{"id":"https://openalex.org/keywords/reductive-groups","display_name":"reductive groups","score":0.9089999794960022}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8485000133514404},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.7182000279426575},{"id":"https://openalex.org/C203701370","wikidata":"https://www.wikidata.org/wiki/Q1047547","display_name":"Algebraically closed field","level":2,"score":0.6018000245094299},{"id":"https://openalex.org/C73301696","wikidata":"https://www.wikidata.org/wiki/Q5469984","display_name":"Formalism (music)","level":3,"score":0.5641999840736389},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5623000264167786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5396999716758728},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5379999876022339},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.5310999751091003},{"id":"https://openalex.org/C187173678","wikidata":"https://www.wikidata.org/wiki/Q1695400","display_name":"Algebraic group","level":3,"score":0.5146999955177307},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.5113999843597412},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4805000126361847},{"id":"https://openalex.org/C179415260","wikidata":"https://www.wikidata.org/wiki/Q1006450","display_name":"Reductive group","level":3,"score":0.4478999972343445},{"id":"https://openalex.org/C81651864","wikidata":"https://www.wikidata.org/wiki/Q874429","display_name":"Group theory","level":2,"score":0.43299999833106995},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C51287006","wikidata":"https://www.wikidata.org/wiki/Q63565120","display_name":"Quotient algebra","level":4,"score":0.384799987077713},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.375},{"id":"https://openalex.org/C171322552","wikidata":"https://www.wikidata.org/wiki/Q3427423","display_name":"Induced representation","level":3,"score":0.36340001225471497},{"id":"https://openalex.org/C46263353","wikidata":"https://www.wikidata.org/wiki/Q4596935","display_name":"2-category","level":4,"score":0.3434000015258789},{"id":"https://openalex.org/C172331165","wikidata":"https://www.wikidata.org/wiki/Q524607","display_name":"General linear group","level":3,"score":0.32839998602867126},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3212999999523163},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3199999928474426},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C114645060","wikidata":"https://www.wikidata.org/wiki/Q5431294","display_name":"Faithful representation","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C11516046","wikidata":"https://www.wikidata.org/wiki/Q1055807","display_name":"Group representation","level":3,"score":0.2883000075817108},{"id":"https://openalex.org/C25971838","wikidata":"https://www.wikidata.org/wiki/Q5277261","display_name":"Dimension of an algebraic variety","level":3,"score":0.28760001063346863},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.28360000252723694},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C199793520","wikidata":"https://www.wikidata.org/wiki/Q4723996","display_name":"Algebraic cycle","level":3,"score":0.275299996137619},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C182327082","wikidata":"https://www.wikidata.org/wiki/Q428290","display_name":"Algebraic closure","level":5,"score":0.26589998602867126},{"id":"https://openalex.org/C130133044","wikidata":"https://www.wikidata.org/wiki/Q1887083","display_name":"Compact group","level":3,"score":0.2653000056743622},{"id":"https://openalex.org/C165761256","wikidata":"https://www.wikidata.org/wiki/Q648995","display_name":"Algebraic variety","level":3,"score":0.2597000002861023},{"id":"https://openalex.org/C33222762","wikidata":"https://www.wikidata.org/wiki/Q321119","display_name":"Identity function","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C72727785","wikidata":"https://www.wikidata.org/wiki/Q2518298","display_name":"Category of sets","level":3,"score":0.25459998846054077}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2609.25148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25148","pdf_url":"https://arxiv.org/pdf/2609.25148","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":"pmh:oai:HAL:hal-05759888v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05759888v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2609.25148","doi":"https://doi.org/10.48550/arxiv.2609.25148","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.25148","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:2609.25148","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.25148","pdf_url":"https://arxiv.org/pdf/2609.25148","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/W7214119776.pdf","grobid_xml":"https://content.openalex.org/works/W7214119776.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2263417265","https://openalex.org/W3004844979","https://openalex.org/W4320843370","https://openalex.org/W4387725441","https://openalex.org/W4387838431","https://openalex.org/W4388184239","https://openalex.org/W4391833461","https://openalex.org/W4402346371","https://openalex.org/W4414903970","https://openalex.org/W6929294159","https://openalex.org/W7138476632"],"related_works":["https://openalex.org/W1964361318","https://openalex.org/W7099810346","https://openalex.org/W4413965796","https://openalex.org/W2798733126","https://openalex.org/W2558554225","https://openalex.org/W1988037106","https://openalex.org/W7128490432","https://openalex.org/W4416331986","https://openalex.org/W2962909873","https://openalex.org/W7095702588"],"abstract_inverted_index":{"In":[0],"this":[1,73],"paper":[2],"we":[3],"present":[4],"a":[5,96],"formalism":[6],"of":[7,15,39,47,52,64,83,93,95,108,118,131],"categorical":[8,70,81],"representation":[9],"theory":[10],"for":[11,44],"affine":[12],"group":[13,54,100],"schemes":[14],"finite":[16],"type":[17],"over":[18,102],"fields":[19],"(both":[20],"in":[21,72,77],"the":[22,37,45,58,80,84,90,116,122,127,132],"weak":[23],"and":[24,49,61,75],"strong":[25],"settings)":[26],"which":[27,56],"applies":[28],"to":[29],"arbitrary":[30],"base":[31],"fields.":[32],"This":[33],"is":[34],"based":[35],"on":[36,89,121],"development":[38],"an":[40,103],"appropriate":[41,91],"$\\infty$-categorical":[42],"setting":[43],"study":[46,69],"representations":[48,94],"Harish-Chandra":[50],"(bi)modules":[51],"such":[53,65],"schemes,":[55],"constitute":[57],"building":[59],"blocks":[60],"basic":[62],"examples":[63],"structures.":[66],"We":[67],"also":[68],"traces":[71],"context,":[74],"show":[76],"particular":[78],"that":[79],"trace":[82],"identity":[85],"morphism,":[86,88],"resp.~Frobenius":[87],"$\\infty$-category":[92,117],"connected":[97],"reductive":[98],"algebraic":[99],"$G$":[101],"algebraically":[104],"closed":[105],"field":[106],"$k$":[107],"positive":[109],"characteristic":[110],"identifies":[111],"(under":[112],"suitable":[113],"assumptions)":[114],"with":[115],"Ind-coherent":[119],"sheaves":[120],"adjoint":[123],"quotient":[124],"$G/G$,":[125],"resp.~of":[126],"fixed":[128],"points":[129],"$G^{\\mathrm{F}}$":[130],"Frobenius.":[133]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-24T00:00:00"}
