{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T02:24:44Z","timestamp":1648952684860},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>K<\/jats:italic> and <jats:italic>K<\/jats:italic>\u2032 be two elliptic fields with complex multiplication over an algebraically closed field <jats:italic>k<\/jats:italic> of characteristic 0. non <jats:italic>k<\/jats:italic>-isomorphic, and let <jats:italic>C<\/jats:italic> and <jats:italic>C<\/jats:italic>\u2032 be two curves with respectively <jats:italic>K<\/jats:italic> and <jats:italic>K<\/jats:italic>\u2032 as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then <jats:italic>K<\/jats:italic> and <jats:italic>K<\/jats:italic>\u2032 are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of <jats:italic>k<\/jats:italic>-algebras.<\/jats:p>","DOI":"10.2178\/jsl\/1190150102","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:13:31Z","timestamp":1197573211000},"page":"635-648","source":"Crossref","is-referenced-by-count":0,"title":["Multiplication complexe et \u00e9quivalence \u00e9l\u00e9mentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)"],"prefix":"10.1017","volume":"67","author":[{"given":"Xavier","family":"Vidaux","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120000966X_ref002","first-page":"948","volume":"51","author":"Duret","year":"1986","journal-title":"Sur la th\u00e9orie \u00e9l\u00e9mentaire des corps de fonctions"},{"key":"S002248120000966X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4752-4"},{"key":"S002248120000966X_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1971323"},{"key":"S002248120000966X_ref009","first-page":"1","article-title":"\u00c9quivalence \u00e9l\u00e9mentaire de corps elliptiques","volume":"330","author":"Vidaux","year":"2000","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences. S\u00e9rie I. Math\u00e9matique"},{"key":"S002248120000966X_ref006","article-title":"Function fields and elementary equivalence","volume":"31","author":"Pierce","year":"1999","journal-title":"Bulletin of the London Mathenatical Society"},{"key":"S002248120000966X_ref003","first-page":"808","volume":"57","author":"Duret","year":"1992","journal-title":"Equivalence \u00e9l\u00e9mentaire et isomorphisme des corps de courbe sur un corps alg\u00e9briquement clos"},{"key":"S002248120000966X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3849-0"},{"key":"S002248120000966X_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"S002248120000966X_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107359901"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120000966X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:06:19Z","timestamp":1557191179000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120000966X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S002248120000966X"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150102","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}