{"id":"https://openalex.org/W2297956301","doi":"https://doi.org/10.1112/s1461157000001455","title":"The Brauer-Manin Obstruction and III[2]","display_name":"The Brauer-Manin Obstruction and III[2]","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2297956301","doi":"https://doi.org/10.1112/s1461157000001455","mag":"2297956301"},"language":"en","primary_location":{"id":"doi:10.1112/s1461157000001455","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001455","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42C530BD1F7C692B7B89B3E857D33DB6/S1461157000001455a.pdf/div-class-title-the-brauer-manin-obstruction-and-iii-2-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":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42C530BD1F7C692B7B89B3E857D33DB6/S1461157000001455a.pdf/div-class-title-the-brauer-manin-obstruction-and-iii-2-div.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000587740","display_name":"Martin Bright","orcid":"https://orcid.org/0000-0002-9139-2614"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"M.J. Bright","raw_affiliation_strings":["Department of Mathematics, University Walk, Bristol BS8 1TWUnited"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University Walk, Bristol BS8 1TWUnited","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022124373","display_name":"Nils Bruin","orcid":"https://orcid.org/0000-0002-0649-2486"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"N. Bruin","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, BurnabyCanada V5A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, BurnabyCanada V5A","institution_ids":["https://openalex.org/I18014758"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041729023","display_name":"E. V. Flynn","orcid":"https://orcid.org/0000-0002-3340-8868"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I4210120676","display_name":"Mathematical Institute of the Slovak Academy of Sciences","ror":"https://ror.org/02fhy7464","country_code":"SK","type":"facility","lineage":["https://openalex.org/I207624831","https://openalex.org/I4210120676"]}],"countries":["GB","SK"],"is_corresponding":false,"raw_author_name":"E.V Flynn","raw_affiliation_strings":["Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford 0X1 3LB, United"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford 0X1 3LB, United","institution_ids":["https://openalex.org/I4210120676","https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027601122","display_name":"Adam Logan","orcid":"https://orcid.org/0000-0001-6157-3521"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"A. Logan","raw_affiliation_strings":["Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5000587740"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":3.0943,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.90932421,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":null,"first_page":"354","last_page":"377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994999766349792,"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":0.9994999766349792,"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/T11130","display_name":"Coding theory and cryptography","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10849","display_name":"Finite Group Theory Research","score":0.968500018119812,"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":0.9209024906158447},{"id":"https://openalex.org/keywords/brauer-group","display_name":"Brauer group","score":0.6540532112121582},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5871827602386475},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5769339799880981},{"id":"https://openalex.org/keywords/quintic-function","display_name":"Quintic function","score":0.5639877915382385},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5020394325256348},{"id":"https://openalex.org/keywords/magma","display_name":"Magma","score":0.48348313570022583},{"id":"https://openalex.org/keywords/locus","display_name":"Locus (genetics)","score":0.48143431544303894},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.4228478968143463},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37959960103034973},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32824236154556274},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12700042128562927},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09240409731864929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9209024906158447},{"id":"https://openalex.org/C62196294","wikidata":"https://www.wikidata.org/wiki/Q900456","display_name":"Brauer group","level":2,"score":0.6540532112121582},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5871827602386475},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5769339799880981},{"id":"https://openalex.org/C124966035","wikidata":"https://www.wikidata.org/wiki/Q33104507","display_name":"Quintic function","level":3,"score":0.5639877915382385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5020394325256348},{"id":"https://openalex.org/C183222429","wikidata":"https://www.wikidata.org/wiki/Q42278","display_name":"Magma","level":3,"score":0.48348313570022583},{"id":"https://openalex.org/C84597430","wikidata":"https://www.wikidata.org/wiki/Q106227","display_name":"Locus (genetics)","level":3,"score":0.48143431544303894},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.4228478968143463},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37959960103034973},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32824236154556274},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12700042128562927},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09240409731864929},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C120806208","wikidata":"https://www.wikidata.org/wiki/Q8072","display_name":"Volcano","level":2,"score":0.0},{"id":"https://openalex.org/C165205528","wikidata":"https://www.wikidata.org/wiki/Q83371","display_name":"Seismology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1112/s1461157000001455","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001455","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42C530BD1F7C692B7B89B3E857D33DB6/S1461157000001455a.pdf/div-class-title-the-brauer-manin-obstruction-and-iii-2-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"}],"best_oa_location":{"id":"doi:10.1112/s1461157000001455","is_oa":true,"landing_page_url":"https://doi.org/10.1112/s1461157000001455","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/42C530BD1F7C692B7B89B3E857D33DB6/S1461157000001455a.pdf/div-class-title-the-brauer-manin-obstruction-and-iii-2-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":[],"funders":[{"id":"https://openalex.org/F4320319997","display_name":"Nuffield Foundation","ror":"https://ror.org/0281jqk77"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2297956301.pdf","grobid_xml":"https://content.openalex.org/works/W2297956301.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W66820687","https://openalex.org/W656995570","https://openalex.org/W956674908","https://openalex.org/W1493035006","https://openalex.org/W1496978265","https://openalex.org/W2003929417","https://openalex.org/W2007109911","https://openalex.org/W2028033673","https://openalex.org/W2040118460","https://openalex.org/W2044546206","https://openalex.org/W2053499741","https://openalex.org/W2099498247","https://openalex.org/W2141049063","https://openalex.org/W2319423512","https://openalex.org/W2584721275","https://openalex.org/W4233143361","https://openalex.org/W6602658953"],"related_works":["https://openalex.org/W607554149","https://openalex.org/W4302555561","https://openalex.org/W4310230578","https://openalex.org/W2329304151","https://openalex.org/W1515531705","https://openalex.org/W2910530413","https://openalex.org/W4226075649","https://openalex.org/W3134603997","https://openalex.org/W2092846166","https://openalex.org/W4283827273"],"abstract_inverted_index":{"We":[0,12,63],"discuss":[1],"the":[2,19,31,42,46,65,68,88],"Brauer-Manin":[3],"obstruction":[4,20],"on":[5],"del":[6],"Pezzo":[7],"surfaces":[8],"of":[9,33,45,49,75,77,82,84,87],"degree":[10],"4.":[11],"outline":[13],"a":[14,103],"detailed":[15],"algorithm":[16],"for":[17,80],"computing":[18],"and":[21],"provide":[22],"associated":[23],"programs":[24],"in":[25,41],"MAGMA.":[26],"This":[27],"is":[28,102],"illustrated":[29],"with":[30,36,67],"computation":[32],"an":[34,37,106],"example":[35],"irreducible":[38,61,107],"cubic":[39,108],"factor":[40],"singular":[43],"locus":[44],"defining":[47],"pencil":[48],"quadrics":[50],"(in":[51],"contrast":[52],"to":[53,71],"previous":[54],"examples,":[55],"which":[56],"had":[57],"at":[58],"worst":[59],"quadratic":[60],"factors).":[62],"exploit":[64],"relationship":[66],"Tate-Shafarevich":[69],"group":[70],"give":[72],"new":[73],"types":[74],"examples":[76],"III":[78],"[2],":[79],"families":[81],"curves":[83],"genus":[85],"2":[86,91],"form":[89],"y":[90],"=":[92],"f":[93,98],"(":[94,99],"x":[95,100],"),":[96],"where":[97],")":[101],"quintic":[104],"containing":[105],"factor.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}