{"id":"https://openalex.org/W7215739099","doi":"https://doi.org/10.48550/arxiv.2610.00189","title":"A characterization of the Ree curve","display_name":"A characterization of the Ree curve","publication_year":2026,"publication_date":"2026-09-17","ids":{"openalex":"https://openalex.org/W7215739099","doi":"https://doi.org/10.48550/arxiv.2610.00189"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.00189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00189","pdf_url":"https://arxiv.org/pdf/2610.00189","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/2610.00189","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014780710","display_name":"Saeed Tafazolian","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Tafazolian, Saeed","raw_affiliation_strings":["IMECC/UNICAMP , R. S\u00e9rgio Buarque de Holanda , 651 , Cidade Universit\u00e1ria \"Zeferino Vaz\" , 13083-859 Campinas , SP , Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMECC/UNICAMP , R. S\u00e9rgio Buarque de Holanda , 651 , Cidade Universit\u00e1ria \"Zeferino Vaz\" , 13083-859 Campinas , SP , Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014780710"],"corresponding_institution_ids":["https://openalex.org/I181391015"],"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":0.9843999743461609,"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":0.9843999743461609,"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":0.0035000001080334187,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.002300000051036477,"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/algebraic-curves-over-finite-fields","display_name":"algebraic curves over finite fields","score":0.6610000133514404},{"id":"https://openalex.org/keywords/isomorphism-characterization","display_name":"isomorphism characterization","score":0.5899999737739563},{"id":"https://openalex.org/keywords/rational-points","display_name":"rational points","score":0.5640000104904175},{"id":"https://openalex.org/keywords/genus","display_name":"genus","score":0.503000020980835},{"id":"https://openalex.org/keywords/projective-curves","display_name":"projective curves","score":0.5709999799728394},{"id":"https://openalex.org/keywords/finite-fields-of-characteristic-3","display_name":"finite fields of characteristic 3","score":0.5329999923706055}],"concepts":[{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.6029999852180481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5343000292778015},{"id":"https://openalex.org/C184389593","wikidata":"https://www.wikidata.org/wiki/Q603159","display_name":"Curve fitting","level":2,"score":0.3878999948501587},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3154999911785126},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2818000018596649},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C90086362","wikidata":"https://www.wikidata.org/wiki/Q1084485","display_name":"Cooling curve","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25859999656677246},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2565000057220459},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.00189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00189","pdf_url":"https://arxiv.org/pdf/2610.00189","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.2610.00189","doi":"https://doi.org/10.48550/arxiv.2610.00189","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.00189","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:2610.00189","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.00189","pdf_url":"https://arxiv.org/pdf/2610.00189","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":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215739099.pdf","grobid_xml":"https://content.openalex.org/works/W7215739099.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2904506240","https://openalex.org/W7214757875","https://openalex.org/W1601929717","https://openalex.org/W4300212128","https://openalex.org/W7131753732","https://openalex.org/W2734408670","https://openalex.org/W1750479067","https://openalex.org/W1569193406","https://openalex.org/W2131709247","https://openalex.org/W1672832481"],"abstract_inverted_index":{"Let":[0],"$q=3q_0^2$,":[1],"where":[2],"$q_0=3^s$":[3],"and":[4,21],"$s\\ge3$.":[5],"We":[6],"prove":[7],"that":[8],"a":[9],"smooth,":[10],"projective,":[11],"geometrically":[12],"irreducible":[13],"curve":[14],"over":[15],"$\\F_q$":[16],"with":[17],"$q^3+1$":[18],"rational":[19],"points":[20],"genus":[22],"\\[":[23],"\\frac32q_0(q-1)(q+q_0+1)":[24],"\\]":[25],"is":[26],"$\\F_q$-isomorphic":[27],"to":[28],"the":[29],"Ree":[30],"curve.":[31]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-03T00:00:00"}