{"id":"https://openalex.org/W2090544989","doi":"https://doi.org/10.1090/s0025-5718-00-01255-2","title":"Computing class fields via the Artin map","display_name":"Computing class fields via the Artin map","publication_year":2000,"publication_date":"2000-03-24","ids":{"openalex":"https://openalex.org/W2090544989","doi":"https://doi.org/10.1090/s0025-5718-00-01255-2","mag":"2090544989"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01255-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01255-2","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01255-2/S0025-5718-00-01255-2.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01255-2/S0025-5718-00-01255-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025858070","display_name":"Claus Fieker","orcid":"https://orcid.org/0000-0002-3420-1498"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Claus Fieker","raw_affiliation_strings":["Fachbereich 3, Mathematik MA 8\u00e2\u0080\u00931, Technische Universit\u00c3\u00a4t Berlin, Stra\u00c3\u009fe des 17. Juni 136, D-10623 Berlin, F.R.G","Fachbereich 3, Mathematik MA 8\u20131, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, D-10623 Berlin, F.R.G"],"affiliations":[{"raw_affiliation_string":"Fachbereich 3, Mathematik MA 8\u00e2\u0080\u00931, Technische Universit\u00c3\u00a4t Berlin, Stra\u00c3\u009fe des 17. Juni 136, D-10623 Berlin, F.R.G","institution_ids":["https://openalex.org/I4577782"]},{"raw_affiliation_string":"Fachbereich 3, Mathematik MA 8\u20131, Technische Universit\u00e4t Berlin, Stra\u00dfe des 17. Juni 136, D-10623 Berlin, F.R.G","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025858070"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":4.0096,"has_fulltext":true,"cited_by_count":47,"citation_normalized_percentile":{"value":0.94312278,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"70","issue":"235","first_page":"1293","last_page":"1303"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9998000264167786,"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":0.9998000264167786,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9991000294685364,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9968000054359436,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8553979992866516},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6145498752593994},{"id":"https://openalex.org/keywords/class-field-theory","display_name":"Class field theory","score":0.5772654414176941},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36230772733688354},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.33062124252319336},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3268049955368042},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11525943875312805},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10540911555290222}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8553979992866516},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6145498752593994},{"id":"https://openalex.org/C195831351","wikidata":"https://www.wikidata.org/wiki/Q1744580","display_name":"Class field theory","level":3,"score":0.5772654414176941},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36230772733688354},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.33062124252319336},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3268049955368042},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11525943875312805},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10540911555290222}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-00-01255-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01255-2","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01255-2/S0025-5718-00-01255-2.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01255-2","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01255-2","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01255-2/S0025-5718-00-01255-2.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.7799999713897705}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2090544989.pdf","grobid_xml":"https://content.openalex.org/works/W2090544989.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1496801598","https://openalex.org/W1509364989","https://openalex.org/W1534790392","https://openalex.org/W1557636054","https://openalex.org/W2019679267","https://openalex.org/W2026360568","https://openalex.org/W2031250754","https://openalex.org/W2036832954","https://openalex.org/W2039576867","https://openalex.org/W2049477745","https://openalex.org/W2911614147","https://openalex.org/W3007836994","https://openalex.org/W3043060850","https://openalex.org/W4247259311","https://openalex.org/W4249589706","https://openalex.org/W4293193836","https://openalex.org/W6659463358"],"related_works":["https://openalex.org/W2938786841","https://openalex.org/W2963037773","https://openalex.org/W2368454205","https://openalex.org/W4297422545","https://openalex.org/W2982120024","https://openalex.org/W2094024499","https://openalex.org/W2370467235","https://openalex.org/W4252613972","https://openalex.org/W1568967829","https://openalex.org/W2802157727"],"abstract_inverted_index":{"Based":[0],"on":[1],"an":[2,50],"explicit":[3,51],"representation":[4],"of":[5,25,44,53],"the":[6,23,26,29,35,38,54],"Artin":[7,55],"map":[8],"for":[9],"Kummer":[10,47],"extensions,":[11],"we":[12,58],"present":[13],"a":[14],"method":[15],"to":[16,34,61],"compute":[17,62],"arbitrary":[18],"class":[19,63],"fields.":[20],"As":[21],"in":[22,65],"proofs":[24],"existence":[27],"theorem,":[28],"problem":[30],"is":[31],"first":[32],"reduced":[33],"case":[36],"where":[37],"field":[39],"contains":[40],"sufficiently":[41],"many":[42],"roots":[43],"unity.":[45],"Using":[46],"theory":[48],"and":[49],"version":[52],"reciprocity":[56],"law":[57],"show":[59],"how":[60],"fields":[64],"this":[66],"case.":[67],"We":[68],"conclude":[69],"with":[70],"several":[71],"examples.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
