{"id":"https://openalex.org/W2520916419","doi":"https://doi.org/10.1090/mcom/3478","title":"Growth of torsion groups of elliptic curves upon base change","display_name":"Growth of torsion groups of elliptic curves upon base change","publication_year":2019,"publication_date":"2019-06-26","ids":{"openalex":"https://openalex.org/W2520916419","doi":"https://doi.org/10.1090/mcom/3478","mag":"2520916419"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3478","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3478","pdf_url":"https://www.ams.org/mcom/2020-89-323/S0025-5718-2019-03478-6/S0025-5718-2019-03478-6.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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2020-89-323/S0025-5718-2019-03478-6/S0025-5718-2019-03478-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037795111","display_name":"Enrique Gonz\u00e1lez\u2013Jim\u00e9nez","orcid":"https://orcid.org/0000-0002-0469-5431"},"institutions":[{"id":"https://openalex.org/I63634437","display_name":"Universidad Aut\u00f3noma de Madrid","ror":"https://ror.org/01cby8j38","country_code":"ES","type":"education","lineage":["https://openalex.org/I63634437"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Enrique Gonz\u00e1lez\u2013Jim\u00e9nez","raw_affiliation_strings":["Departamento de Matem\u00c3\u00a1ticas, Universidad Aut\u00c3\u00b3noma de Madrid, Madrid, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00c3\u00a1ticas, Universidad Aut\u00c3\u00b3noma de Madrid, Madrid, Spain","institution_ids":["https://openalex.org/I63634437"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081214859","display_name":"Filip Najman","orcid":"https://orcid.org/0000-0002-0994-0846"},"institutions":[{"id":"https://openalex.org/I181343428","display_name":"University of Zagreb","ror":"https://ror.org/00mv6sv71","country_code":"HR","type":"education","lineage":["https://openalex.org/I181343428"]}],"countries":["HR"],"is_corresponding":false,"raw_author_name":"Filip Najman","raw_affiliation_strings":["Department of Mathematics, University of Zagreb, Bijeni\u00c4\u008dka cesta 30, 10000 Zagreb, Croatia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Zagreb, Bijeni\u00c4\u008dka cesta 30, 10000 Zagreb, Croatia","institution_ids":["https://openalex.org/I181343428"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037795111"],"corresponding_institution_ids":["https://openalex.org/I63634437"],"apc_list":null,"apc_paid":null,"fwci":7.5999,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.97966715,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"89","issue":"323","first_page":"1457","last_page":"1485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9994000196456909,"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":0.9994000196456909,"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/mathematics","display_name":"Mathematics","score":0.7770895957946777},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.6640447378158569},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.6087523698806763},{"id":"https://openalex.org/keywords/algebraic-number-field","display_name":"Algebraic number field","score":0.571635365486145},{"id":"https://openalex.org/keywords/base-change","display_name":"Base change","score":0.5249329209327698},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49306604266166687},{"id":"https://openalex.org/keywords/twists-of-curves","display_name":"Twists of curves","score":0.473073810338974},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.4624732732772827},{"id":"https://openalex.org/keywords/sato\u2013tate-conjecture","display_name":"Sato\u2013Tate conjecture","score":0.4448014497756958},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.43156689405441284},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.42794692516326904},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4136312007904053},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2898624539375305},{"id":"https://openalex.org/keywords/schoofs-algorithm","display_name":"Schoof's algorithm","score":0.2525278925895691},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22613343596458435},{"id":"https://openalex.org/keywords/quarter-period","display_name":"Quarter period","score":0.15112504363059998},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14206627011299133}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7770895957946777},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.6640447378158569},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.6087523698806763},{"id":"https://openalex.org/C12657307","wikidata":"https://www.wikidata.org/wiki/Q616608","display_name":"Algebraic number field","level":2,"score":0.571635365486145},{"id":"https://openalex.org/C103751382","wikidata":"https://www.wikidata.org/wiki/Q4866384","display_name":"Base change","level":2,"score":0.5249329209327698},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49306604266166687},{"id":"https://openalex.org/C131182338","wikidata":"https://www.wikidata.org/wiki/Q7858596","display_name":"Twists of curves","level":5,"score":0.473073810338974},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4624732732772827},{"id":"https://openalex.org/C162355417","wikidata":"https://www.wikidata.org/wiki/Q2993331","display_name":"Sato\u2013Tate conjecture","level":5,"score":0.4448014497756958},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.43156689405441284},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.42794692516326904},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4136312007904053},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2898624539375305},{"id":"https://openalex.org/C121444067","wikidata":"https://www.wikidata.org/wiki/Q2835817","display_name":"Schoof's algorithm","level":4,"score":0.2525278925895691},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22613343596458435},{"id":"https://openalex.org/C197875053","wikidata":"https://www.wikidata.org/wiki/Q7269266","display_name":"Quarter period","level":3,"score":0.15112504363059998},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14206627011299133},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/mcom/3478","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3478","pdf_url":"https://www.ams.org/mcom/2020-89-323/S0025-5718-2019-03478-6/S0025-5718-2019-03478-6.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"},{"id":"pmh:oai:arXiv.org:1609.02515","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.02515","pdf_url":"https://arxiv.org/pdf/1609.02515","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"},{"id":"pmh:oai:repositorio.uam.es:10486/710746","is_oa":true,"landing_page_url":"http://hdl.handle.net/10486/710746","pdf_url":null,"source":{"id":"https://openalex.org/S4306400963","display_name":"Biblos-e Archivo (Universidad Aut\u00f3noma de Madrid)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63634437","host_organization_name":"Universidad Aut\u00f3noma de Madrid","host_organization_lineage":["https://openalex.org/I63634437"],"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":null,"raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1090/mcom/3478","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3478","pdf_url":"https://www.ams.org/mcom/2020-89-323/S0025-5718-2019-03478-6/S0025-5718-2019-03478-6.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":[],"awards":[{"id":"https://openalex.org/G1401252225","display_name":null,"funder_award_id":"IP-2018-01-1313","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"},{"id":"https://openalex.org/G5450880337","display_name":null,"funder_award_id":"IP-2018-01-1313","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G7501275679","display_name":null,"funder_award_id":"MTM2015-68524-P","funder_id":"https://openalex.org/F4320322674","funder_display_name":"Hrvatska Zaklada za Znanost"},{"id":"https://openalex.org/G7742415711","display_name":null,"funder_award_id":"MTM2015-68524-P","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320322674","display_name":"Hrvatska Zaklada za Znanost","ror":"https://ror.org/03n51vw80"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2520916419.pdf","grobid_xml":"https://content.openalex.org/works/W2520916419.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W1508466895","https://openalex.org/W1516318957","https://openalex.org/W1598030683","https://openalex.org/W1612004367","https://openalex.org/W1625091117","https://openalex.org/W1637562839","https://openalex.org/W1931259144","https://openalex.org/W1962852960","https://openalex.org/W1988379376","https://openalex.org/W1990539329","https://openalex.org/W2000856267","https://openalex.org/W2001572759","https://openalex.org/W2011844852","https://openalex.org/W2042927258","https://openalex.org/W2050464828","https://openalex.org/W2070421272","https://openalex.org/W2073082930","https://openalex.org/W2082955605","https://openalex.org/W2083355759","https://openalex.org/W2085262455","https://openalex.org/W2092097669","https://openalex.org/W2118169332","https://openalex.org/W2155694865","https://openalex.org/W2177408741","https://openalex.org/W2205586407","https://openalex.org/W2240841908","https://openalex.org/W2335187233","https://openalex.org/W2411861508","https://openalex.org/W2517959248","https://openalex.org/W2950581790","https://openalex.org/W2962817287","https://openalex.org/W2963422318","https://openalex.org/W2963707516","https://openalex.org/W3098850051","https://openalex.org/W3104298675","https://openalex.org/W3104561728","https://openalex.org/W4288055696","https://openalex.org/W4301187166"],"related_works":["https://openalex.org/W4302766435","https://openalex.org/W2950987065","https://openalex.org/W2111232859","https://openalex.org/W4287990591","https://openalex.org/W4226318811","https://openalex.org/W3098079019","https://openalex.org/W4293482052","https://openalex.org/W2964131781","https://openalex.org/W2110244809","https://openalex.org/W2520916419"],"abstract_inverted_index":{"We":[0,353],"study":[1],"how":[2],"the":[3,201,348,351],"torsion":[4,23,203],"of":[5,50,70,278,323,350],"elliptic":[6,160,280,325],"curves":[7,161],"over":[8,74,176,283,327],"number":[9,27,51,258],"fields":[10,52],"grows":[11],"upon":[12],"base":[13,276,321],"change,":[14],"and":[15,260],"in":[16,199],"particular":[17],"prove":[18,354],"various":[19],"necessary":[20],"conditions":[21],"for":[22,46,158,347],"growth.":[24],"For":[25],"a":[26,47,257,275,320],"field":[28,259],"<inline-formula":[29,53,75,95,162,177,205,243,261,284,306,328,356],"content-type=\"math/mathml\">":[30,54,76,96,163,178,206,244,262,285,307,329,357],"<mml:math":[31,55,77,97,164,179,207,245,263,286,308,330,358],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[32,56,78,98,165,180,208,246,264,287,309,331,359],"alttext=\"upper":[33,57,79,99,166,181,209,247,265,310,360],"F\">":[34,80,182],"<mml:semantics>":[35,59,81,123,168,183,220,249,267,291,312,335,385],"<mml:mi>F</mml:mi>":[36,82,141,184],"<mml:annotation":[37,61,83,151,170,185,235,251,269,297,314,341],"encoding=\"application/x-tex\">F</mml:annotation>":[38,84,186],"</mml:semantics>":[39,63,85,155,172,187,238,253,271,300,316,344],"</mml:math>":[40,64,86,156,173,188,239,254,272,301,317,345],"</inline-formula>":[41,65,87,157,174,189,240,255,273,302,318,346],",":[42,66,241],"we":[43],"show":[44],"that":[45,94,305,355],"large":[48],"set":[49],"L\">":[58],"<mml:mi>L</mml:mi>":[60,128],"encoding=\"application/x-tex\">L</mml:annotation>":[62],"whose":[67],"Galois":[68],"group":[69],"their":[71],"normal":[72],"closure":[73],"has":[88],"certain":[89],"properties,":[90],"it":[91],"will":[92],"hold":[93],"E":[100,113,210,361,374],"left-parenthesis":[101,114,211,362,375],"upper":[102,112,115,212,289,333,363,373,377],"L":[103],"right-parenthesis":[104,117,214,365,379],"Subscript":[105,118,215,366,380],"t":[106,119,216,367,381],"o":[107,120,217,368,382],"r":[108,121,218,369,383],"s":[109,370],"Baseline":[110,371],"equals":[111,372],"F":[116],"s\">":[122,219,384],"<mml:mrow>":[124,221,386],"<mml:mi>E</mml:mi>":[125,138,169,222,268,313,387,400],"<mml:mo":[126,130,139,143,223,227,388,392,401,409],"stretchy=\"false\">(</mml:mo>":[127,140,224,389,402],"<mml:msub>":[129,142,226,391,408],"stretchy=\"false\">)</mml:mo>":[131,144,228,393,410],"<mml:mrow":[132,145,229,292,336,394,403,411],"class=\"MJX-TeXAtom-ORD\">":[133,146,230,293,337,395,404,412],"<mml:mi>tors</mml:mi>":[134,147,231,396,413],"</mml:mrow>":[135,148,150,232,234,296,340,397,407,414,416],"</mml:msub>":[136,149,233,398,415],"<mml:mo>=</mml:mo>":[137,399],"encoding=\"application/x-tex\">E(L)_{\\operatorname":[152],"{tors}}=E(F)_{\\operatorname":[153],"{tors}}</mml:annotation>":[154,237],"all":[159],"E\">":[167,266,311],"encoding=\"application/x-tex\">E</mml:annotation>":[171,270,315],"defined":[175,282],".":[190,303],"Our":[191],"methods":[192],"turn":[193],"out":[194],"to":[195],"be":[196],"particularly":[197],"useful":[198],"studying":[200],"possible":[202],"groups":[204],"K":[213,364],"<mml:mi>K</mml:mi>":[225,250,390],"encoding=\"application/x-tex\">E(K)_{\\operatorname":[236],"where":[242],"K\">":[248],"encoding=\"application/x-tex\">K</mml:annotation>":[252],"is":[256,274,319],"change":[277,322],"an":[279,324],"curve":[281,326],"alttext=\"double-struck":[288,332],"Q\">":[290,334],"<mml:mi":[294,338,405],"mathvariant=\"double-struck\">Q</mml:mi>":[295,339,406],"encoding=\"application/x-tex\">\\mathbb":[298,342],"{Q}</mml:annotation>":[299,343],"Suppose":[304],"remainder":[349],"abstract.":[352],"double-struck":[376],"Q":[378]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-23T06:14:38.165362","created_date":"2025-10-10T00:00:00"}