On fields of definition of torsion points of elliptic curves with complex multiplication
For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all ca...
Gespeichert in:
| Veröffentlicht in: | Proceedings of the American Mathematical Society 2011-06, Vol.139 (6), p.1961-1969 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1969 |
|---|---|
| container_issue | 6 |
| container_start_page | 1961 |
| container_title | Proceedings of the American Mathematical Society |
| container_volume | 139 |
| creator | DIEULEFAIT, LUIS GONZÁLEZ-JIMÉNEZ, ENRIQUE URROZ, JORGE JIMÉNEZ |
| description | For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM. |
| doi_str_mv | 10.1090/S0002-9939-2010-10621-4 |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_csuc_</sourceid><recordid>TN_cdi_csuc_recercat_oai_recercat_cat_2072_194353</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>41291753</jstor_id><sourcerecordid>41291753</sourcerecordid><originalsourceid>FETCH-LOGICAL-a443t-7226f42441920b9b8f1bafd67c19fe96cab2aed8536debee07fef2e73c4771223</originalsourceid><addsrcrecordid>eNqNkMtOwzAQRS0EEqXwCYhsWBo8EzeOl6jiJVXqApDYWY5jC1dpEtkpj78nj6psWVj21Z07Mz6EXAG7ASbZ7QtjDKmUqaTIgFFgGQLlR2QGLM9plmN2TGaHolNyFuOmlyC5mJH3dZ04b6syJo1LSut87Tvf1IPqmhCHZ9v4uht9W1W-7bxJzC582ph8-e4jMc22rex3st1VnW8rb_TQ4JycOF1Fe7G_5-Tt4f51-URX68fn5d2Kas7TjgrEzHHkHCSyQha5g0K7MhMGpLMyM7pAbct8kWalLaxlwlmHVqSGCwGI6ZzA1NfEnVHBGhv6BVSj_Z8YDjKBqv9zukj7jNhnQhNjsE61wW91-FHA1ABVjVDVwEsNUNUIVfE-eT0lWx2NrlzQtfHxEEcOKYcF6-sup7pN7CkefA4oQYwb4OTrbfz38F_kV5D0</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On fields of definition of torsion points of elliptic curves with complex multiplication</title><source>American Mathematical Society Publications (Freely Accessible)</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>JSTOR Mathematics & Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>American Mathematical Society Publications</source><source>Recercat</source><creator>DIEULEFAIT, LUIS ; GONZÁLEZ-JIMÉNEZ, ENRIQUE ; URROZ, JORGE JIMÉNEZ</creator><creatorcontrib>DIEULEFAIT, LUIS ; GONZÁLEZ-JIMÉNEZ, ENRIQUE ; URROZ, JORGE JIMÉNEZ</creatorcontrib><description>For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.</description><identifier>ISSN: 0002-9939</identifier><identifier>EISSN: 1088-6826</identifier><identifier>DOI: 10.1090/S0002-9939-2010-10621-4</identifier><identifier>CODEN: PAMYAR</identifier><language>eng</language><publisher>Providence, RI: American Mathematical Society</publisher><subject>11 Number theory ; 11F Discontinuous groups and automorphic forms ; 11G Arithmetic algebraic geometry (Diophantine geometry) ; Algebra ; Algebraic geometry ; Classificació AMS ; Corbes el·líptiques ; Curves ; Curves, Elliptic ; Exact sciences and technology ; Factorization ; Galois theory ; Galois, Teoria de ; General mathematics ; General, history and biography ; Information representations ; Integers ; Matemàtiques i estadística ; Mathematical tables ; Mathematics ; Number theory ; Polynomials ; Prime numbers ; Sciences and techniques of general use ; Teoria de nombres ; Torsion ; Torsió ; Àlgebra ; Àrees temàtiques de la UPC</subject><ispartof>Proceedings of the American Mathematical Society, 2011-06, Vol.139 (6), p.1961-1969</ispartof><rights>Copyright 2010, American Mathematical Society</rights><rights>2011 American Mathematical Society</rights><rights>2015 INIST-CNRS</rights><rights>Attribution-NonCommercial-NoDerivs 3.0 Spain info:eu-repo/semantics/openAccess <a href="http://creativecommons.org/licenses/by-nc-nd/3.0/es/">http://creativecommons.org/licenses/by-nc-nd/3.0/es/</a></rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a443t-7226f42441920b9b8f1bafd67c19fe96cab2aed8536debee07fef2e73c4771223</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttp://www.ams.org/jourcgi/jour-getitem?pii=S0002-9939-2010-10621-4S0002-9939-2010-10621-4.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttp://www.ams.org/jourcgi/jour-getitem?pii=S0002-9939-2010-10621-4$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>68,69,230,315,781,785,804,833,886,23329,23333,26979,27929,27930,58022,58026,58255,58259,77841,77843,77851,77853</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=24134150$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>DIEULEFAIT, LUIS</creatorcontrib><creatorcontrib>GONZÁLEZ-JIMÉNEZ, ENRIQUE</creatorcontrib><creatorcontrib>URROZ, JORGE JIMÉNEZ</creatorcontrib><title>On fields of definition of torsion points of elliptic curves with complex multiplication</title><title>Proceedings of the American Mathematical Society</title><description>For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.</description><subject>11 Number theory</subject><subject>11F Discontinuous groups and automorphic forms</subject><subject>11G Arithmetic algebraic geometry (Diophantine geometry)</subject><subject>Algebra</subject><subject>Algebraic geometry</subject><subject>Classificació AMS</subject><subject>Corbes el·líptiques</subject><subject>Curves</subject><subject>Curves, Elliptic</subject><subject>Exact sciences and technology</subject><subject>Factorization</subject><subject>Galois theory</subject><subject>Galois, Teoria de</subject><subject>General mathematics</subject><subject>General, history and biography</subject><subject>Information representations</subject><subject>Integers</subject><subject>Matemàtiques i estadística</subject><subject>Mathematical tables</subject><subject>Mathematics</subject><subject>Number theory</subject><subject>Polynomials</subject><subject>Prime numbers</subject><subject>Sciences and techniques of general use</subject><subject>Teoria de nombres</subject><subject>Torsion</subject><subject>Torsió</subject><subject>Àlgebra</subject><subject>Àrees temàtiques de la UPC</subject><issn>0002-9939</issn><issn>1088-6826</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>XX2</sourceid><recordid>eNqNkMtOwzAQRS0EEqXwCYhsWBo8EzeOl6jiJVXqApDYWY5jC1dpEtkpj78nj6psWVj21Z07Mz6EXAG7ASbZ7QtjDKmUqaTIgFFgGQLlR2QGLM9plmN2TGaHolNyFuOmlyC5mJH3dZ04b6syJo1LSut87Tvf1IPqmhCHZ9v4uht9W1W-7bxJzC582ph8-e4jMc22rex3st1VnW8rb_TQ4JycOF1Fe7G_5-Tt4f51-URX68fn5d2Kas7TjgrEzHHkHCSyQha5g0K7MhMGpLMyM7pAbct8kWalLaxlwlmHVqSGCwGI6ZzA1NfEnVHBGhv6BVSj_Z8YDjKBqv9zukj7jNhnQhNjsE61wW91-FHA1ABVjVDVwEsNUNUIVfE-eT0lWx2NrlzQtfHxEEcOKYcF6-sup7pN7CkefA4oQYwb4OTrbfz38F_kV5D0</recordid><startdate>20110601</startdate><enddate>20110601</enddate><creator>DIEULEFAIT, LUIS</creator><creator>GONZÁLEZ-JIMÉNEZ, ENRIQUE</creator><creator>URROZ, JORGE JIMÉNEZ</creator><general>American Mathematical Society</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>XX2</scope></search><sort><creationdate>20110601</creationdate><title>On fields of definition of torsion points of elliptic curves with complex multiplication</title><author>DIEULEFAIT, LUIS ; GONZÁLEZ-JIMÉNEZ, ENRIQUE ; URROZ, JORGE JIMÉNEZ</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a443t-7226f42441920b9b8f1bafd67c19fe96cab2aed8536debee07fef2e73c4771223</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>11 Number theory</topic><topic>11F Discontinuous groups and automorphic forms</topic><topic>11G Arithmetic algebraic geometry (Diophantine geometry)</topic><topic>Algebra</topic><topic>Algebraic geometry</topic><topic>Classificació AMS</topic><topic>Corbes el·líptiques</topic><topic>Curves</topic><topic>Curves, Elliptic</topic><topic>Exact sciences and technology</topic><topic>Factorization</topic><topic>Galois theory</topic><topic>Galois, Teoria de</topic><topic>General mathematics</topic><topic>General, history and biography</topic><topic>Information representations</topic><topic>Integers</topic><topic>Matemàtiques i estadística</topic><topic>Mathematical tables</topic><topic>Mathematics</topic><topic>Number theory</topic><topic>Polynomials</topic><topic>Prime numbers</topic><topic>Sciences and techniques of general use</topic><topic>Teoria de nombres</topic><topic>Torsion</topic><topic>Torsió</topic><topic>Àlgebra</topic><topic>Àrees temàtiques de la UPC</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DIEULEFAIT, LUIS</creatorcontrib><creatorcontrib>GONZÁLEZ-JIMÉNEZ, ENRIQUE</creatorcontrib><creatorcontrib>URROZ, JORGE JIMÉNEZ</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Recercat</collection><jtitle>Proceedings of the American Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DIEULEFAIT, LUIS</au><au>GONZÁLEZ-JIMÉNEZ, ENRIQUE</au><au>URROZ, JORGE JIMÉNEZ</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On fields of definition of torsion points of elliptic curves with complex multiplication</atitle><jtitle>Proceedings of the American Mathematical Society</jtitle><date>2011-06-01</date><risdate>2011</risdate><volume>139</volume><issue>6</issue><spage>1961</spage><epage>1969</epage><pages>1961-1969</pages><issn>0002-9939</issn><eissn>1088-6826</eissn><coden>PAMYAR</coden><abstract>For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves; in particular, we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.</abstract><cop>Providence, RI</cop><pub>American Mathematical Society</pub><doi>10.1090/S0002-9939-2010-10621-4</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0002-9939 |
| ispartof | Proceedings of the American Mathematical Society, 2011-06, Vol.139 (6), p.1961-1969 |
| issn | 0002-9939 1088-6826 |
| language | eng |
| recordid | cdi_csuc_recercat_oai_recercat_cat_2072_194353 |
| source | American Mathematical Society Publications (Freely Accessible); Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; American Mathematical Society Publications; Recercat |
| subjects | 11 Number theory 11F Discontinuous groups and automorphic forms 11G Arithmetic algebraic geometry (Diophantine geometry) Algebra Algebraic geometry Classificació AMS Corbes el·líptiques Curves Curves, Elliptic Exact sciences and technology Factorization Galois theory Galois, Teoria de General mathematics General, history and biography Information representations Integers Matemàtiques i estadística Mathematical tables Mathematics Number theory Polynomials Prime numbers Sciences and techniques of general use Teoria de nombres Torsion Torsió Àlgebra Àrees temàtiques de la UPC |
| title | On fields of definition of torsion points of elliptic curves with complex multiplication |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-11T21%3A45%3A31IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_csuc_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20fields%20of%20definition%20of%20torsion%20points%20of%20elliptic%20curves%20with%20complex%20multiplication&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.au=DIEULEFAIT,%20LUIS&rft.date=2011-06-01&rft.volume=139&rft.issue=6&rft.spage=1961&rft.epage=1969&rft.pages=1961-1969&rft.issn=0002-9939&rft.eissn=1088-6826&rft.coden=PAMYAR&rft_id=info:doi/10.1090/S0002-9939-2010-10621-4&rft_dat=%3Cjstor_csuc_%3E41291753%3C/jstor_csuc_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=41291753&rfr_iscdi=true |