{"id":"https://openalex.org/W1970574333","doi":"https://doi.org/10.1112/s1461157009000576","title":"Explicit computations of Serre\u2019s obstruction for genus-3 curves and application to optimal curves","display_name":"Explicit computations of Serre\u2019s obstruction for genus-3 curves and application to optimal curves","publication_year":2010,"publication_date":"2010-05-01","ids":{"openalex":"https://openalex.org/W1970574333","doi":"https://doi.org/10.1112/s1461157009000576","mag":"1970574333"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157009000576","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157009000576","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BAD4ED6221A2BA633A8B6A1A8BB5F94B/S1461157009000576a.pdf/div-class-title-explicit-computations-of-serre-s-obstruction-for-genus-3-curves-and-application-to-optimal-curves-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BAD4ED6221A2BA633A8B6A1A8BB5F94B/S1461157009000576a.pdf/div-class-title-explicit-computations-of-serre-s-obstruction-for-genus-3-curves-and-application-to-optimal-curves-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114026163","display_name":"Christophe Ritzenthaler","orcid":null},"institutions":[{"id":"https://openalex.org/I4210126368","display_name":"Institut de Recherche Dupuy de L\u00f4me","ror":"https://ror.org/03011gg73","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I180375564","https://openalex.org/I201181511","https://openalex.org/I2802204017","https://openalex.org/I4210095849","https://openalex.org/I4210126368","https://openalex.org/I4210145102","https://openalex.org/I4210148559","https://openalex.org/I4405260085"]},{"id":"https://openalex.org/I4210138206","display_name":"Institut de Math\u00e9matiques de Marseille","ror":"https://ror.org/042h2y225","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210138206","https://openalex.org/I4210141950","https://openalex.org/I4210142724"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Christophe Ritzenthaler","raw_affiliation_strings":["Institut de math\u00e9matiques de Luminy, UMR 6206, 163 Avenue de Luminy Case 90713288 Marseille, France","Institut de math\u00e9matiques de Luminy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de math\u00e9matiques de Luminy, UMR 6206, 163 Avenue de Luminy Case 90713288 Marseille, France","institution_ids":["https://openalex.org/I4210138206"]},{"raw_affiliation_string":"Institut de math\u00e9matiques de Luminy","institution_ids":["https://openalex.org/I4210126368"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5114026163"],"corresponding_institution_ids":["https://openalex.org/I4210126368","https://openalex.org/I4210138206"],"apc_list":null,"apc_paid":null,"fwci":1.4951,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.79627255,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":null,"first_page":"192","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998999834060669,"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":0.9998999834060669,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9836000204086304,"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/mathematics","display_name":"Mathematics","score":0.9106786251068115},{"id":"https://openalex.org/keywords/complex-multiplication","display_name":"Complex multiplication","score":0.7937387228012085},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.7406078577041626},{"id":"https://openalex.org/keywords/indecomposable-module","display_name":"Indecomposable module","score":0.6736924648284912},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6267410516738892},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.6188591718673706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5190142393112183},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.508141040802002},{"id":"https://openalex.org/keywords/hyperelliptic-curve","display_name":"Hyperelliptic curve","score":0.42556047439575195},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.2938764691352844},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.23572000861167908}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9106786251068115},{"id":"https://openalex.org/C80146680","wikidata":"https://www.wikidata.org/wiki/Q2654923","display_name":"Complex multiplication","level":3,"score":0.7937387228012085},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.7406078577041626},{"id":"https://openalex.org/C157480366","wikidata":"https://www.wikidata.org/wiki/Q2499534","display_name":"Indecomposable module","level":2,"score":0.6736924648284912},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6267410516738892},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.6188591718673706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5190142393112183},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.508141040802002},{"id":"https://openalex.org/C11074058","wikidata":"https://www.wikidata.org/wiki/Q850110","display_name":"Hyperelliptic curve","level":3,"score":0.42556047439575195},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2938764691352844},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.23572000861167908},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1112/s1461157009000576","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157009000576","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BAD4ED6221A2BA633A8B6A1A8BB5F94B/S1461157009000576a.pdf/div-class-title-explicit-computations-of-serre-s-obstruction-for-genus-3-curves-and-application-to-optimal-curves-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0901.2920","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0901.2920","pdf_url":"https://arxiv.org/pdf/0901.2920","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:10.1112/s1461157009000576","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157009000576","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/BAD4ED6221A2BA633A8B6A1A8BB5F94B/S1461157009000576a.pdf/div-class-title-explicit-computations-of-serre-s-obstruction-for-genus-3-curves-and-application-to-optimal-curves-div.pdf","source":{"id":"https://openalex.org/S118668765","display_name":"LMS Journal of Computation and Mathematics","issn_l":"1461-1570","issn":["1461-1570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311874","host_organization_name":"London Mathematical Society","host_organization_lineage":["https://openalex.org/P4310311874"],"host_organization_lineage_names":["London Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"LMS Journal of Computation and Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G664156994","display_name":"Courbes Hyperelliptiques : Isog\u00e9nies et Comptage","funder_award_id":"ANR-09-BLAN-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320273","display_name":"University of Cambridge","ror":"https://ror.org/013meh722"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970574333.pdf","grobid_xml":"https://content.openalex.org/works/W1970574333.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1482156586","https://openalex.org/W1512075513","https://openalex.org/W1523988862","https://openalex.org/W1526722268","https://openalex.org/W1545876477","https://openalex.org/W1611566840","https://openalex.org/W1641463135","https://openalex.org/W1641551699","https://openalex.org/W1674256678","https://openalex.org/W1980143629","https://openalex.org/W1983253134","https://openalex.org/W1993930656","https://openalex.org/W2011073488","https://openalex.org/W2022224108","https://openalex.org/W2041442561","https://openalex.org/W2050381181","https://openalex.org/W2069122556","https://openalex.org/W2070761677","https://openalex.org/W2088328421","https://openalex.org/W2089508405","https://openalex.org/W2131709247","https://openalex.org/W2322172566","https://openalex.org/W2322604914","https://openalex.org/W2328344866","https://openalex.org/W2330356368","https://openalex.org/W2497459839","https://openalex.org/W2614117299","https://openalex.org/W2949827758","https://openalex.org/W3170013141","https://openalex.org/W4293045476"],"related_works":["https://openalex.org/W3029460748","https://openalex.org/W1510953762","https://openalex.org/W4237505298","https://openalex.org/W2995607861","https://openalex.org/W1870827190","https://openalex.org/W2963089085","https://openalex.org/W1849004580","https://openalex.org/W2127683917","https://openalex.org/W2592919142","https://openalex.org/W2045416952"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"k":[2,28,42],"be":[3,13,46],"a":[4,17,25,32,39,61],"field":[5],"of":[6,50,53,57,60,83,101,105],"characteristic":[7],"other":[8],"than":[9],"2.":[10],"There":[11],"can":[12,45],"an":[14,84],"obstruction":[15],"to":[16,69,95],"principally":[18,74],"polarized":[19,75],"abelian":[20,76],"threefold":[21],"(":[22],"A":[23],",":[24,29,37],")":[26],"over":[27,34,41],"which":[30,78],"is":[31],"Jacobian":[33,40],"$\\bar":[35],"{k}$":[36],"being":[38],";":[43],"this":[44,71],"computed":[47],"in":[48],"terms":[49],"the":[51,54,58,80,99],"rationality":[52],"square":[55],"root":[56],"value":[59],"certain":[62],"Siegel":[63],"modular":[64],"form.":[65],"We":[66,90],"show":[67],"how":[68],"do":[70],"explicitly":[72],"for":[73],"threefolds":[77],"are":[79],"third":[81],"power":[82],"elliptic":[85],"curve":[86],"with":[87],"complex":[88],"multiplication.":[89],"use":[91],"our":[92],"numerical":[93],"results":[94],"prove":[96],"or":[97],"refute":[98],"existence":[100],"some":[102],"optimal":[103],"curves":[104],"genus":[106],"3.":[107]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}