{"id":"https://openalex.org/W7214932209","doi":"https://doi.org/10.48550/arxiv.2609.37975","title":"Computing residual representations of abelian threefolds with imaginary multiplication","display_name":"Computing residual representations of abelian threefolds with imaginary multiplication","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214932209","doi":"https://doi.org/10.48550/arxiv.2609.37975"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37975","pdf_url":"https://arxiv.org/pdf/2609.37975","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/2609.37975","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080372795","display_name":"Shiva Chidambaram","orcid":"https://orcid.org/0000-0001-7325-6363","observed_orcids":["https://orcid.org/0000-0001-7325-6363"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chidambaram, Shiva","raw_affiliation_strings":["University of Wisconsin-Madison , 480 Lincoln Dr , Madison , WI 53706 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison , 480 Lincoln Dr , Madison , WI 53706 USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087189668","display_name":"Pip Goodman","orcid":"https://orcid.org/0000-0001-6735-2367","observed_orcids":["https://orcid.org/0000-0001-6735-2367"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Goodman, Pip","raw_affiliation_strings":["Max Planck Institute for Mathematics , Vivatsgasse 7 , 53111 Bonn , Ger - many","University of Wisconsin-Madison , 480 Lincoln Dr , Madison , WI 53706 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics , Vivatsgasse 7 , 53111 Bonn , Ger - many","institution_ids":["https://openalex.org/I4210119712"]},{"raw_affiliation_string":"University of Wisconsin-Madison , 480 Lincoln Dr , Madison , WI 53706 USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.57669997215271,"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":0.57669997215271,"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":0.413100004196167,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0008999999845400453,"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/abelian-threefolds","display_name":"abelian threefolds","score":0.906000018119812},{"id":"https://openalex.org/keywords/endomorphism-algebras","display_name":"endomorphism algebras","score":0.6930000185966492},{"id":"https://openalex.org/keywords/jacobians-of-curves","display_name":"Jacobians of curves","score":0.8629999756813049},{"id":"https://openalex.org/keywords/shimura-curves","display_name":"Shimura curves","score":0.7720000147819519},{"id":"https://openalex.org/keywords/quaternionic-multiplication","display_name":"quaternionic multiplication","score":0.9340000152587891},{"id":"https://openalex.org/keywords/isogenies","display_name":"isogenies","score":0.5509999990463257}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8914999961853027},{"id":"https://openalex.org/C116858840","wikidata":"https://www.wikidata.org/wiki/Q1340800","display_name":"Endomorphism","level":2,"score":0.7305999994277954},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.6234999895095825},{"id":"https://openalex.org/C145899342","wikidata":"https://www.wikidata.org/wiki/Q3427418","display_name":"Galois module","level":2,"score":0.5733000040054321},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5680999755859375},{"id":"https://openalex.org/C167300717","wikidata":"https://www.wikidata.org/wiki/Q3554814","display_name":"Abelian variety of CM-type","level":5,"score":0.5618000030517578},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4779999852180481},{"id":"https://openalex.org/C195637984","wikidata":"https://www.wikidata.org/wiki/Q4791130","display_name":"Arithmetic of abelian varieties","level":5,"score":0.4697999954223633},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4009000062942505},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3935000002384186},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3702000081539154},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.3571999967098236},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C200681373","wikidata":"https://www.wikidata.org/wiki/Q1260803","display_name":"Rank of an abelian group","level":4,"score":0.34880000352859497},{"id":"https://openalex.org/C2779765290","wikidata":"https://www.wikidata.org/wiki/Q1674414","display_name":"Isogeny","level":3,"score":0.33570000529289246},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C57637645","wikidata":"https://www.wikidata.org/wiki/Q318705","display_name":"Abelian extension","level":3,"score":0.33230000734329224},{"id":"https://openalex.org/C95136341","wikidata":"https://www.wikidata.org/wiki/Q625519","display_name":"Quadratic field","level":4,"score":0.32519999146461487},{"id":"https://openalex.org/C103738662","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Field extension","level":3,"score":0.3190999925136566},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3043999969959259},{"id":"https://openalex.org/C81008192","wikidata":"https://www.wikidata.org/wiki/Q1017231","display_name":"Elementary abelian group","level":3,"score":0.29679998755455017},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.28189998865127563},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C11074058","wikidata":"https://www.wikidata.org/wiki/Q850110","display_name":"Hyperelliptic curve","level":3,"score":0.273499995470047},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C2777283802","wikidata":"https://www.wikidata.org/wiki/Q2042963","display_name":"Picard group","level":3,"score":0.26930001378059387},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2614000141620636}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37975","pdf_url":"https://arxiv.org/pdf/2609.37975","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.2609.37975","doi":"https://doi.org/10.48550/arxiv.2609.37975","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37975","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37975","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37975","pdf_url":"https://arxiv.org/pdf/2609.37975","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/W7214932209.pdf","grobid_xml":"https://content.openalex.org/works/W7214932209.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4283744845","https://openalex.org/W7202255343"],"related_works":["https://openalex.org/W4415981133","https://openalex.org/W950571710","https://openalex.org/W1977808506","https://openalex.org/W2022034584","https://openalex.org/W4407185606","https://openalex.org/W4407251979","https://openalex.org/W7222089025","https://openalex.org/W2791372728","https://openalex.org/W4300167641","https://openalex.org/W1970574333"],"abstract_inverted_index":{"Let":[0,7],"$M$":[1,16],"be":[2,9,63,219],"an":[3,104,115],"imaginary":[4,92],"quadratic":[5],"field.":[6,207],"$A$":[8],"a":[10,108,162,205],"polarised":[11,229],"abelian":[12,89,230],"threefold":[13],"defined":[14,120],"over":[15,121,165],"with":[17,91,135,232],"geometric":[18],"endomorphism":[19,37,136,197],"algebra":[20,137,198],"isomorphic":[21],"to":[22,30,62,79,95,113,153,180,195,218,226],"$M$.":[23],"We":[24,51,102],"study":[25],"residual":[26,46,59],"Galois":[27,60,163],"representations":[28,47,61],"attached":[29],"$A$.":[31],"In":[32],"particular,":[33],"we":[34,75],"describe":[35],"the":[36,40,45,56,130,155,181,212],"field":[38],"and":[39,65,94,216],"natural":[41],"restrictions":[42],"placed":[43],"on":[44,211],"by":[48],"their":[49],"endomorphisms.":[50],"then":[52],"devise":[53],"criteria":[54],"for":[55,70,146,167],"image":[57,141],"of":[58,81,98,107,117,125,132,158,183,188,199,223],"large,":[64],"provide":[66],"efficient":[67],"algorithms":[68,176],"suitable":[69],"large":[71,143],"scale":[72],"calculations.":[73],"Subsequently,":[74],"apply":[76],"this":[77],"algorithm":[78],"millions":[80],"curves":[82,190,210],"in":[83,129],"several":[84,184],"families,":[85],"whose":[86,191],"Jacobians":[87,124],"are":[88],"threefolds":[90],"multiplication,":[93],"Sutherland's":[96],"dataset":[97],"$7$-smooth":[99],"Picard":[100,109,189,213],"curves.":[101,221],"produce":[103],"explicit":[105],"example":[106],"curve":[110],"which":[111,202],"appears":[112],"have":[114,139,196],"isogeny":[116],"degree":[118],"$13$":[119],"$\\mathbb{Q}(\u03b6_3)$.":[122],"The":[123],"all":[126,168],"other":[127],"curves,":[128],"range":[131],"our":[133],"computation":[134],"$M$,":[138],"mod-$\\ell$":[140],"as":[142,144,161],"possible":[145],"any":[147],"prime":[148],"$\\ell>7$.":[149],"This":[150],"allows":[151],"us":[152,179],"realise":[154],"group":[156,164],"$\u0393\\mathrm{U}_3(\\ell)$":[157],"unitary":[159],"semisimilitudes":[160],"$\\mathbb{Q}$":[166],"$\\ell":[169],"\\not\\equiv":[170],"1,":[171],"25,":[172],"121":[173],"\\pmod{168}$.":[174],"Our":[175],"also":[177],"led":[178],"discovery":[182],"interesting":[185],"rational":[186],"families":[187],"generic":[192],"members":[193],"appear":[194,217,225],"dimension":[200],"$6$":[201],"is":[203],"not":[204],"CM":[206],"These":[208],"represent":[209],"modular":[214],"surface":[215],"Shimura":[220],"Some":[222],"them":[224],"parametrise":[227],"non-principally":[228],"surfaces":[231],"quaternionic":[233],"multiplication.":[234]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
