{"id":"https://openalex.org/W2007461989","doi":"https://doi.org/10.1090/s0025-5718-08-02165-0","title":"Genus two curves with quaternionic multiplication and modular Jacobian","display_name":"Genus two curves with quaternionic multiplication and modular Jacobian","publication_year":2008,"publication_date":"2008-10-14","ids":{"openalex":"https://openalex.org/W2007461989","doi":"https://doi.org/10.1090/s0025-5718-08-02165-0","mag":"2007461989"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02165-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02165-0","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02165-0/S0025-5718-08-02165-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02165-0/S0025-5718-08-02165-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Josep Gonz\u00e1lez","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Josep Gonz\u00e1lez","raw_affiliation_strings":["Escola Polit\u00c3\u00a8cnica Superior d\u00e2\u0080\u0099Engenyeria de Vilanova i la Geltr\u00c3\u00ba, Avda Victor Balaguer s/n, 08800 Vilanova i la Geltr\u00c3\u00ba, Spain"],"affiliations":[{"raw_affiliation_string":"Escola Polit\u00c3\u00a8cnica Superior d\u00e2\u0080\u0099Engenyeria de Vilanova i la Geltr\u00c3\u00ba, Avda Victor Balaguer s/n, 08800 Vilanova i la Geltr\u00c3\u00ba, Spain","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Jordi Gu\u00e0rdia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jordi Gu\u00e0rdia","raw_affiliation_strings":["Escola Polit\u00c3\u00a8cnica Superior d\u00e2\u0080\u0099Engenyeria de Vilanova i la Geltr\u00c3\u00ba, Avda Victor Balaguer s/n, 08800 Vilanova i la Geltr\u00c3\u00ba, Spain"],"affiliations":[{"raw_affiliation_string":"Escola Polit\u00c3\u00a8cnica Superior d\u00e2\u0080\u0099Engenyeria de Vilanova i la Geltr\u00c3\u00ba, Avda Victor Balaguer s/n, 08800 Vilanova i la Geltr\u00c3\u00ba, Spain","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.09160369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"78","issue":"265","first_page":"575","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4000000059604645,"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":0.4000000059604645,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.33399999141693115,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.04190000146627426,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/multiplication","display_name":"Multiplication (music)","score":0.7570000290870667},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7378000020980835},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"Complex multiplication","score":0.7286999821662903},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.6017000079154968},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5939000248908997},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.5264999866485596},{"id":"https://openalex.org/keywords/modular-design","display_name":"Modular design","score":0.47200000286102295},{"id":"https://openalex.org/keywords/modular-form","display_name":"Modular form","score":0.4230000078678131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.927299976348877},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7570000290870667},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7378000020980835},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.7286999821662903},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.6017000079154968},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5939000248908997},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5383999943733215},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.47200000286102295},{"id":"https://openalex.org/C75764964","wikidata":"https://www.wikidata.org/wiki/Q870797","display_name":"Modular form","level":2,"score":0.4230000078678131},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40639999508857727},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.38769999146461487},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3391999900341034},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.3328000009059906},{"id":"https://openalex.org/C25398135","wikidata":"https://www.wikidata.org/wiki/Q7269569","display_name":"Quaternionic representation","level":4,"score":0.329800009727478},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.31619998812675476},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2980000078678131},{"id":"https://openalex.org/C32049820","wikidata":"https://www.wikidata.org/wiki/Q319400","display_name":"Modular arithmetic","level":3,"score":0.2840999960899353},{"id":"https://openalex.org/C180375552","wikidata":"https://www.wikidata.org/wiki/Q2635326","display_name":"Structured program theorem","level":2,"score":0.2572999894618988}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-08-02165-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02165-0","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02165-0/S0025-5718-08-02165-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0805.1302","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0805.1302","pdf_url":"https://arxiv.org/pdf/0805.1302","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02165-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02165-0","pdf_url":"https://www.ams.org/mcom/2009-78-265/S0025-5718-08-02165-0/S0025-5718-08-02165-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2007461989.pdf","grobid_xml":"https://content.openalex.org/works/W2007461989.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W6631530779","https://openalex.org/W6632610091","https://openalex.org/W6730572539","https://openalex.org/W6814941904"],"related_works":[],"abstract_inverted_index":{"We":[0,31],"describe":[1],"a":[2,24,45],"method":[3],"to":[4,23,53,67],"determine":[5],"all":[6],"the":[7,14],"isomorphism":[8],"classes":[9],"of":[10,13,35],"principal":[11],"polarizations":[12],"modular":[15],"abelian":[16],"surfaces":[17],"$A_f$":[18,36,51],"with":[19,37],"quaternionic":[20,38,62],"multiplication":[21,39,63],"attached":[22],"normalized":[25],"newform":[26],"$f$":[27],"without":[28],"complex":[29],"multiplication.":[30],"include":[32],"an":[33],"example":[34],"for":[40],"which":[41],"we":[42,57],"find":[43],"numerically":[44],"curve":[46],"$C$":[47],"whose":[48],"Jacobian":[49],"is":[50,65],"up":[52],"numerical":[54],"approximation,":[55],"and":[56,64],"prove":[58],"that":[59],"it":[60],"has":[61],"isogenous":[66],"$A_f$.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}