{"id":"https://openalex.org/W7224879640","doi":"https://doi.org/10.48550/arxiv.2610.40335","title":"Galois module structure of Deligne--Lusztig varieties for $\\mathrm{GL}_3$","display_name":"Galois module structure of Deligne--Lusztig varieties for $\\mathrm{GL}_3$","publication_year":2026,"publication_date":"2026-10-29","ids":{"openalex":"https://openalex.org/W7224879640","doi":"https://doi.org/10.48550/arxiv.2610.40335"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.40335","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40335","pdf_url":"https://arxiv.org/pdf/2610.40335","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/2610.40335","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138141123","display_name":"Adithya Sathyanarayana","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sathyanarayana, Adithya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5138141123"],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9365000128746033,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9365000128746033,"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":0.046300001442432404,"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/T10849","display_name":"Finite Group Theory Research","score":0.004100000020116568,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/galois-module-structure","display_name":"Galois module structure","score":0.8619999885559082},{"id":"https://openalex.org/keywords/deligne-lusztig-varieties","display_name":"Deligne-Lusztig varieties","score":0.9729999899864197},{"id":"https://openalex.org/keywords/gl-3","display_name":"GL3","score":0.7870000004768372},{"id":"https://openalex.org/keywords/lefschetz-number","display_name":"Lefschetz number","score":0.8830000162124634},{"id":"https://openalex.org/keywords/equivariant-euler-characteristic","display_name":"equivariant Euler characteristic","score":0.7910000085830688},{"id":"https://openalex.org/keywords/virtual-representation","display_name":"virtual representation","score":0.6769999861717224},{"id":"https://openalex.org/keywords/type-a2","display_name":"type A2","score":0.5659999847412109},{"id":"https://openalex.org/keywords/coherent-cohomology","display_name":"coherent cohomology","score":0.7319999933242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8944000005722046},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5723999738693237},{"id":"https://openalex.org/C2779165322","wikidata":"https://www.wikidata.org/wiki/Q546145","display_name":"Compactification (mathematics)","level":2,"score":0.5109999775886536},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.46239998936653137},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.46209999918937683},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.45669999718666077},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C182349385","wikidata":"https://www.wikidata.org/wiki/Q382839","display_name":"Galois cohomology","level":3,"score":0.3806000053882599},{"id":"https://openalex.org/C145899342","wikidata":"https://www.wikidata.org/wiki/Q3427418","display_name":"Galois module","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C4017995","wikidata":"https://www.wikidata.org/wiki/Q595298","display_name":"Sheaf","level":2,"score":0.35440000891685486},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3474999964237213},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3181999921798706},{"id":"https://openalex.org/C93067474","wikidata":"https://www.wikidata.org/wiki/Q1493952","display_name":"Sheaf cohomology","level":4,"score":0.31529998779296875},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C26204071","wikidata":"https://www.wikidata.org/wiki/Q2020004","display_name":"Galois extension","level":3,"score":0.2680000066757202},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.2581999897956848}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.40335","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40335","pdf_url":"https://arxiv.org/pdf/2610.40335","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.2610.40335","doi":"https://doi.org/10.48550/arxiv.2610.40335","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.40335","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:2610.40335","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.40335","pdf_url":"https://arxiv.org/pdf/2610.40335","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/W7224879640.pdf","grobid_xml":"https://content.openalex.org/works/W7224879640.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1777000415","https://openalex.org/W6889724284","https://openalex.org/W4409672302","https://openalex.org/W2041709407","https://openalex.org/W4392795470","https://openalex.org/W2952780409","https://openalex.org/W7046123600","https://openalex.org/W2963707759","https://openalex.org/W4416100792","https://openalex.org/W2005854287"],"abstract_inverted_index":{"Let":[0],"$\\overline{\\mathbf{Y}}(w)\\to\\overline{\\mathbf{X}}(w)$":[1],"be":[2],"the":[3,16,20,23,29,33,47,52,60,76,83,92,97,109],"ramified":[4],"Galois":[5],"cover":[6],"of":[7,13,22,32,36,44,55,63,66,82,85,96],"compactified":[8],"Deligne--Lusztig":[9,64],"varieties.":[10],"Our":[11],"objects":[12],"study":[14],"are":[15],"Lefschetz":[17,39,77],"numbers":[18,40,78],"for":[19,41,75,79],"action":[21],"finite":[24],"covering":[25,110],"group":[26],"$T^{wF}$":[27,45],"on":[28],"coherent":[30],"cohomology":[31,57],"structure":[34],"sheaf":[35],"$\\overline{\\mathbf{Y}}(w)$.":[37],"The":[38],"all":[42],"elements":[43],"determine":[46],"virtual":[48,106],"$T^{wF}$-representation":[49],"given":[50],"by":[51],"alternating":[53],"sum":[54],"these":[56],"groups.":[58],"In":[59],"two":[61],"cases":[62],"surfaces":[65],"type":[67],"$A_2$":[68],"and":[69],"${}^{2}A_2$,":[70],"we":[71],"give":[72],"explicit":[73],"formulas":[74],"a":[80,105],"generator":[81],"stabilizer":[84],"an":[86],"irreducible":[87],"component.":[88],"It":[89],"follows":[90],"that":[91],"equivariant":[93],"Euler":[94],"characteristic":[95],"compactification":[98],"$\\overline{\\mathbf{Y}}(w)$":[99],"is":[100],"not":[101],"virtually":[102],"free":[103],"as":[104],"module":[107],"over":[108],"group.":[111]},"counts_by_year":[],"updated_date":"2026-11-02T09:45:03.842371","created_date":"2026-10-31T00:00:00"}