{"id":"https://openalex.org/W4240616454","doi":"https://doi.org/10.4171/owr/2018/25","title":"Field Arithmetic","display_name":"Field Arithmetic","publication_year":2019,"publication_date":"2019-04-11","ids":{"openalex":"https://openalex.org/W4240616454","doi":"https://doi.org/10.4171/owr/2018/25"},"language":"en","primary_location":{"id":"doi:10.4171/owr/2018/25","doi":"https://doi.org/10.4171/owr/2018/25","is_oa":false,"landing_page_url":"https://doi.org/10.4171/owr/2018/25","pdf_url":null,"source":{"id":"https://openalex.org/S159844132","display_name":"Oberwolfach Reports","issn_l":"1660-8933","issn":["1660-8933","1660-8941"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/I4389425263","host_organization_name":"EMS Press","host_organization_lineage":["https://openalex.org/I4389425263"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Oberwolfach Reports","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://oa.tib.eu/renate/handle/123456789/13359","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052276618","display_name":"Lior Bary\u2010Soroker","orcid":"https://orcid.org/0000-0002-1303-247X","observed_orcids":["https://orcid.org/0000-0002-1303-247X"]},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Lior Bary-Soroker","raw_affiliation_strings":["Tel Aviv University, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tel Aviv University, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030439284","display_name":"Florian Pop","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Florian Pop","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, USA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010455415","display_name":"Jakob Stix","orcid":"https://orcid.org/0000-0002-0198-4107","observed_orcids":["https://orcid.org/0000-0002-0198-4107"]},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jakob Stix","raw_affiliation_strings":["Goethe-Universit\u00e4t Frankfurt, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Goethe-Universit\u00e4t Frankfurt, Germany","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"2","first_page":"1517","last_page":"1577"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.4609000086784363,"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":0.4609000086784363,"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":0.3865000009536743,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.09700000286102295,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/field-arithmetic","display_name":"field arithmetic","score":0.9869999885559082},{"id":"https://openalex.org/keywords/absolute-galois-group","display_name":"absolute Galois group","score":0.9879999756813049},{"id":"https://openalex.org/keywords/decidability","display_name":"decidability","score":0.7129999995231628},{"id":"https://openalex.org/keywords/undecidability","display_name":"undecidability","score":0.8690000176429749},{"id":"https://openalex.org/keywords/model-theory","display_name":"model theory","score":0.7879999876022339},{"id":"https://openalex.org/keywords/profinite-groups","display_name":"profinite groups","score":0.8059999942779541},{"id":"https://openalex.org/keywords/algebraic-number-theory","display_name":"algebraic number theory","score":0.7559999823570251}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7423429489135742},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5878141522407532},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5285263061523438},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5113165378570557},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.489997535943985},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4778263568878174},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.4701690077781677},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.43239665031433105},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.42586496472358704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3733259439468384},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2759910225868225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08369150757789612}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.4171/owr/2018/25","doi":"https://doi.org/10.4171/owr/2018/25","is_oa":false,"landing_page_url":"https://doi.org/10.4171/owr/2018/25","pdf_url":null,"source":{"id":"https://openalex.org/S159844132","display_name":"Oberwolfach Reports","issn_l":"1660-8933","issn":["1660-8933","1660-8941"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core"],"host_organization":"https://openalex.org/I4389425263","host_organization_name":"EMS Press","host_organization_lineage":["https://openalex.org/I4389425263"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Oberwolfach Reports","raw_type":"journal-article"},{"id":"pmh:oai:oa.tib.eu:123456789/13359","doi":null,"is_oa":true,"landing_page_url":"https://oa.tib.eu/renate/handle/123456789/13359","pdf_url":null,"source":{"id":"https://openalex.org/S7407052981","display_name":"RENATE","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Oberwolfach reports : OWR","raw_type":"doc-type:Article"},{"id":"doi:10.34657/12389","doi":"https://doi.org/10.34657/12389","is_oa":true,"landing_page_url":"https://doi.org/10.34657/12389","pdf_url":null,"source":{"id":"https://openalex.org/S7407052981","display_name":"RENATE","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"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":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:oa.tib.eu:123456789/13359","doi":null,"is_oa":true,"landing_page_url":"https://oa.tib.eu/renate/handle/123456789/13359","pdf_url":null,"source":{"id":"https://openalex.org/S7407052981","display_name":"RENATE","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Oberwolfach reports : OWR","raw_type":"doc-type:Article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W6946357684","https://openalex.org/W4390109867","https://openalex.org/W1973102026","https://openalex.org/W2910635008","https://openalex.org/W2109074235","https://openalex.org/W7221551346","https://openalex.org/W7036256359","https://openalex.org/W6948298426","https://openalex.org/W2087145162","https://openalex.org/W2608252761"],"abstract_inverted_index":{"Field":[0],"Arithmetic":[1],"studies":[2],"the":[3,42],"interrelation":[4],"between":[5],"arithmetic":[6,31],"properties":[7],"of":[8,23,41,48],"fields":[9],"and":[10,34,37,51],"their":[11],"absolute":[12],"Galois":[13],"groups.":[14],"It":[15],"is":[16],"an":[17],"interdisciplinary":[18],"area":[19],"that":[20],"uses":[21],"methods":[22],"algebraic":[24,29],"number":[25],"theory,":[26],"commutative":[27],"algebra,":[28],"geometry,":[30,32],"finite":[33],"profinite":[35],"groups,":[36],"nonarchimedean":[38],"analysis.":[39],"Some":[40],"results":[43,55],"are":[44],"motivated":[45],"by":[46],"questions":[47],"model":[49],"theory":[50],"used":[52],"to":[53],"establish":[54],"in":[56],"(un-)decidability.":[57]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-05-12T00:00:00"}