{"id":"https://openalex.org/W7222409005","doi":"https://doi.org/10.48550/arxiv.2610.21488","title":"Smoothness of Shortest Isogenies to Frobenius Conjugates","display_name":"Smoothness of Shortest Isogenies to Frobenius Conjugates","publication_year":2026,"publication_date":"2026-10-15","ids":{"openalex":"https://openalex.org/W7222409005","doi":"https://doi.org/10.48550/arxiv.2610.21488"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.21488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21488","pdf_url":"https://arxiv.org/pdf/2610.21488","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/2610.21488","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158919909","display_name":"Yi Ouyang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ouyang, Yi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5158903134","display_name":"Wei Wei","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158930149","display_name":"Zheng Xu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.6723999977111816,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.6723999977111816,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.24899999797344208,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.025299999862909317,"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/supersingular-curves","display_name":"supersingular elliptic curves","score":0.9660000205039978},{"id":"https://openalex.org/keywords/isogenies","display_name":"isogenies","score":0.8939999938011169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8810999989509583},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.597000002861023},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.520799994468689},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C2778153370","wikidata":"https://www.wikidata.org/wiki/Q2896709","display_name":"Endomorphism ring","level":3,"score":0.4708999991416931},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.45879998803138733},{"id":"https://openalex.org/C157567686","wikidata":"https://www.wikidata.org/wiki/Q7644139","display_name":"Supersingular elliptic curve","level":3,"score":0.42399999499320984},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40779998898506165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3959999978542328},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38960000872612},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.3873000144958496},{"id":"https://openalex.org/C197336794","wikidata":"https://www.wikidata.org/wiki/Q5161150","display_name":"Conjugate","level":2,"score":0.29440000653266907},{"id":"https://openalex.org/C68363185","wikidata":"https://www.wikidata.org/wiki/Q180969","display_name":"Algebraic geometry","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.2583000063896179},{"id":"https://openalex.org/C86177461","wikidata":"https://www.wikidata.org/wiki/Q837551","display_name":"Frobenius theorem (differential topology)","level":5,"score":0.25600001215934753},{"id":"https://openalex.org/C161491579","wikidata":"https://www.wikidata.org/wiki/Q858656","display_name":"Commutative ring","level":3,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.21488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21488","pdf_url":"https://arxiv.org/pdf/2610.21488","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.2610.21488","doi":"https://doi.org/10.48550/arxiv.2610.21488","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.21488","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:2610.21488","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.21488","pdf_url":"https://arxiv.org/pdf/2610.21488","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/W7222409005.pdf","grobid_xml":"https://content.openalex.org/works/W7222409005.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W3196798028","https://openalex.org/W7128591411"],"related_works":["https://openalex.org/W7213876711","https://openalex.org/W7169566054","https://openalex.org/W3115412413","https://openalex.org/W4386843007","https://openalex.org/W4409253210","https://openalex.org/W2953201355","https://openalex.org/W2791851483","https://openalex.org/W3116436840","https://openalex.org/W2794648107","https://openalex.org/W2993730380"],"abstract_inverted_index":{"Let":[0],"$E$":[1,25,84],"be":[2,18],"chosen":[3],"uniformly":[4],"from":[5,24],"the":[6,19,35,47,73],"geometric":[7],"isomorphism":[8],"classes":[9],"of":[10,22,38,68,79],"supersingular":[11,48],"elliptic":[12],"curves":[13],"over":[14],"$\\overline{\\mathbb{F}}_p$":[15],"and":[16,40,85],"$\u03b4_E$":[17,39],"minimum":[20],"degree":[21,80],"isogenies":[23],"to":[26],"its":[27],"Frobenius":[28],"conjugate":[29],"$E^{(p)}$.":[30,86],"We":[31,54],"establish":[32,56],"bounds":[33],"for":[34,72],"smoothness":[36],"probability":[37,74],"hence":[41],"affirm":[42],"Wesolowski's":[43],"$p^{1/3+o(1)}$":[44],"attack":[45],"on":[46],"endomorphism":[49],"ring":[50],"problem":[51],"is":[52],"unconditional.":[53],"also":[55],"a":[57,62,76],"uniform":[58],"asymptotic":[59],"formula,":[60],"with":[61],"main":[63],"term":[64],"expressed":[65],"in":[66],"terms":[67],"Dirichlet":[69],"$L$":[70],"values,":[71],"that":[75],"connection":[77],"isogeny":[78],"$n$":[81],"exists":[82],"between":[83]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-17T00:00:00"}
