{"id":"https://openalex.org/W7225783605","doi":"https://doi.org/10.20944/preprints202611.1098.v1","title":"Integral Parahoric Comparison and Diagonal Bockstein Obstruction Cancellation at p = 41","display_name":"Integral Parahoric Comparison and Diagonal Bockstein Obstruction Cancellation at p = 41","publication_year":2026,"publication_date":"2026-11-11","ids":{"openalex":"https://openalex.org/W7225783605","doi":"https://doi.org/10.20944/preprints202611.1098.v1"},"language":"en","primary_location":{"id":"doi:10.20944/preprints202611.1098.v1","doi":"https://doi.org/10.20944/preprints202611.1098.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202611.1098.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.20944/preprints202611.1098.v1","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101961197","display_name":"Tao Lin","orcid":"https://orcid.org/0000-0002-6450-9629","observed_orcids":["https://orcid.org/0000-0002-6450-9629","https://orcid.org/0009-0004-1291-515X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lin Tao","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-1291-515X","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5101961197"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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":0.9990000128746033,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9990000128746033,"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":0.0003000000142492354,"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":9.999999747378752e-05,"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":[],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8149999976158142},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6492000222206116},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5121999979019165},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4388999938964844},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.3971000015735626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3898000121116638},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3824999928474426},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37119999527931213},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C191832335","wikidata":"https://www.wikidata.org/wiki/Q4262191","display_name":"Fourier integral operator","level":3,"score":0.296099990606308},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.29260000586509705},{"id":"https://openalex.org/C184311908","wikidata":"https://www.wikidata.org/wiki/Q425432","display_name":"Laurent series","level":2,"score":0.28940001130104065},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2736000120639801},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C54865166","wikidata":"https://www.wikidata.org/wiki/Q844937","display_name":"Multiple integral","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.20944/preprints202611.1098.v1","doi":"https://doi.org/10.20944/preprints202611.1098.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202611.1098.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"}],"best_oa_location":{"id":"doi:10.20944/preprints202611.1098.v1","doi":"https://doi.org/10.20944/preprints202611.1098.v1","is_oa":true,"landing_page_url":"https://doi.org/10.20944/preprints202611.1098.v1","pdf_url":null,"source":{"id":"https://openalex.org/S6309402219","display_name":"Preprints.org","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"posted-content"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Let":[0],"$p=41$":[1],"and":[2,10,65,140,155],"consider":[3],"the":[4,25,29,33,41,53,70,83,102,108,116,121,150],"integral":[5,50,67,138],"chamber-glued":[6],"parahoric":[7],"source":[8,56,80,139],"$J_{\\mathrm{geom}}$":[9],"hyperspecial":[11],"target":[12,71,92,105,110],"lattice":[13,73],"$L_K$":[14],"associated":[15],"with":[16,57,74,97,120],"a":[17,61,75],"specified":[18],"principal":[19],"series":[20],"of":[21,28,32,52,69],"$GSp_4(Q_{41})$.":[22],"We":[23,47],"determine":[24],"$H$-fixed":[26],"subspace":[27],"residual":[30],"kernel":[31],"summation":[34],"map":[35],"$J_{\\mathrm{geom}}/41J_{\\mathrm{geom}}\\to":[36],"L_K/41L_K$,":[37],"where":[38],"$H$":[39],"is":[40,106,133],"elementary":[42],"abelian":[43],"Klingen":[44],"unipotent":[45],"quotient.":[46],"establish":[48],"an":[49,66,112],"comparison":[51],"original":[54],"42-leaf":[55],"its":[58],"normalized":[59],"presentation,":[60],"restricted":[62],"Bockstein":[63],"criterion,":[64],"identification":[68],"relation":[72,117],"three-step":[76],"intertwiner":[77],"image.":[78],"The":[79,131,137],"class":[81],"in":[82],"40-dimensional":[84],"Levi":[85],"constituent":[86],"has":[87,111],"two":[88],"diagonal":[89,109],"components.":[90],"Their":[91],"contributions":[93],"combine":[94],"as":[95,161],"$g_Y^{\\mathrm{diag}}=g_Y^{(v=5)}+\\Delta$":[96],"$\\Delta=-41e_2+41e_{1054}$":[98],"modulo":[99],"$41^2$;":[100],"although":[101],"isolated":[103],"single-channel":[104],"obstructed,":[107],"explicit":[113],"preimage":[114],"under":[115],"matrix.":[118],"Together":[119],"corresponding":[122],"$20$-dimensional":[123],"constituent,":[124],"this":[125,145],"yields":[126],"$V_{41}^{H}\\cong":[127],"X_{20}\\oplus":[128],"Y_{40},\\qquad":[129],"\\dim_{F_{41}}V_{41}^{H}=60.$":[130],"argument":[132],"confined":[134],"to":[135],"$p=41$.":[136],"Levi-module":[141],"statements":[142],"needed":[143],"for":[144],"conclusion":[146],"are":[147,158],"proved":[148],"within":[149],"appendices.":[151],"Reproducible":[152],"finite-ring":[153],"computations":[154],"falsification":[156],"tests":[157],"supplied":[159],"separately":[160],"supporting":[162],"evidence.":[163]},"counts_by_year":[],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2026-11-12T00:00:00"}