The Eisenstein ideal with squarefree level
We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number \(p>3\) and a squarefree number \(N\) satisfying certain conditions, we study the Eisenstein part of the \(p\)-adic Hecke algebra for \(\Gamma_0(N)\), and sh...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2021-01 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Wake, Preston Wang-Erickson, Carl |
| description | We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number \(p>3\) and a squarefree number \(N\) satisfying certain conditions, we study the Eisenstein part of the \(p\)-adic Hecke algebra for \(\Gamma_0(N)\), and show that it is a local complete intersection and isomorphic to a pseudodeformation ring. We also show that in certain cases, the Eisenstein ideal is not principal and that the cuspidal quotient of the Hecke algebra is not Gorenstein. As a corollary, we prove that "multiplicity one" fails for the modular Jacobian in these cases. In a particular case, this proves a conjecture of Ribet. |
| doi_str_mv | 10.48550/arxiv.1804.06400 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_1804_06400</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2072208482</sourcerecordid><originalsourceid>FETCH-LOGICAL-a522-a40a044e0a2248d4e4c2b0f4989ab9132d6cde1c949dc5b3c438482c12d0652d3</originalsourceid><addsrcrecordid>eNotj81Kw0AURgdBsNQ-gCsD7oTEmzt30slSSrVCwU32YTJzQ6fEtJ1Jqr69_XH1bQ6H7wjxkENGWil4MeHHH7NcA2VQEMCNmKCUeaoJ8U7MYtwCABZzVEpOxHO14WTpI_dxYN8n3rHpkm8_bJJ4GE3gNjAnHR-5uxe3rekiz_53Kqq3ZbVYpevP94_F6zo1CjE1BAaIGAwiaUdMFhtoqdSlacpcoius49yWVDqrGmlJatJoc3RQKHRyKh6v2ktIvQ_-y4Tf-hxUX4JOxNOV2IfdYeQ41NvdGPrTpxphjghnofwDZXJMDw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2072208482</pqid></control><display><type>article</type><title>The Eisenstein ideal with squarefree level</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Wake, Preston ; Wang-Erickson, Carl</creator><creatorcontrib>Wake, Preston ; Wang-Erickson, Carl</creatorcontrib><description>We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number \(p>3\) and a squarefree number \(N\) satisfying certain conditions, we study the Eisenstein part of the \(p\)-adic Hecke algebra for \(\Gamma_0(N)\), and show that it is a local complete intersection and isomorphic to a pseudodeformation ring. We also show that in certain cases, the Eisenstein ideal is not principal and that the cuspidal quotient of the Hecke algebra is not Gorenstein. As a corollary, we prove that "multiplicity one" fails for the modular Jacobian in these cases. In a particular case, this proves a conjecture of Ribet.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1804.06400</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Mathematics - Number Theory ; Prime numbers ; Quotients</subject><ispartof>arXiv.org, 2021-01</ispartof><rights>2021. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,784,885,27925</link.rule.ids><backlink>$$Uhttps://doi.org/10.48550/arXiv.1804.06400$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1016/j.aim.2020.107543$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Wake, Preston</creatorcontrib><creatorcontrib>Wang-Erickson, Carl</creatorcontrib><title>The Eisenstein ideal with squarefree level</title><title>arXiv.org</title><description>We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number \(p>3\) and a squarefree number \(N\) satisfying certain conditions, we study the Eisenstein part of the \(p\)-adic Hecke algebra for \(\Gamma_0(N)\), and show that it is a local complete intersection and isomorphic to a pseudodeformation ring. We also show that in certain cases, the Eisenstein ideal is not principal and that the cuspidal quotient of the Hecke algebra is not Gorenstein. As a corollary, we prove that "multiplicity one" fails for the modular Jacobian in these cases. In a particular case, this proves a conjecture of Ribet.</description><subject>Mathematics - Number Theory</subject><subject>Prime numbers</subject><subject>Quotients</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GOX</sourceid><recordid>eNotj81Kw0AURgdBsNQ-gCsD7oTEmzt30slSSrVCwU32YTJzQ6fEtJ1Jqr69_XH1bQ6H7wjxkENGWil4MeHHH7NcA2VQEMCNmKCUeaoJ8U7MYtwCABZzVEpOxHO14WTpI_dxYN8n3rHpkm8_bJJ4GE3gNjAnHR-5uxe3rekiz_53Kqq3ZbVYpevP94_F6zo1CjE1BAaIGAwiaUdMFhtoqdSlacpcoius49yWVDqrGmlJatJoc3RQKHRyKh6v2ktIvQ_-y4Tf-hxUX4JOxNOV2IfdYeQ41NvdGPrTpxphjghnofwDZXJMDw</recordid><startdate>20210119</startdate><enddate>20210119</enddate><creator>Wake, Preston</creator><creator>Wang-Erickson, Carl</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210119</creationdate><title>The Eisenstein ideal with squarefree level</title><author>Wake, Preston ; Wang-Erickson, Carl</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a522-a40a044e0a2248d4e4c2b0f4989ab9132d6cde1c949dc5b3c438482c12d0652d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Number Theory</topic><topic>Prime numbers</topic><topic>Quotients</topic><toplevel>online_resources</toplevel><creatorcontrib>Wake, Preston</creatorcontrib><creatorcontrib>Wang-Erickson, Carl</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Access via ProQuest (Open Access)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wake, Preston</au><au>Wang-Erickson, Carl</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Eisenstein ideal with squarefree level</atitle><jtitle>arXiv.org</jtitle><date>2021-01-19</date><risdate>2021</risdate><eissn>2331-8422</eissn><abstract>We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number \(p>3\) and a squarefree number \(N\) satisfying certain conditions, we study the Eisenstein part of the \(p\)-adic Hecke algebra for \(\Gamma_0(N)\), and show that it is a local complete intersection and isomorphic to a pseudodeformation ring. We also show that in certain cases, the Eisenstein ideal is not principal and that the cuspidal quotient of the Hecke algebra is not Gorenstein. As a corollary, we prove that "multiplicity one" fails for the modular Jacobian in these cases. In a particular case, this proves a conjecture of Ribet.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.1804.06400</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2021-01 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_arxiv_primary_1804_06400 |
| source | arXiv.org; Free E- Journals |
| subjects | Mathematics - Number Theory Prime numbers Quotients |
| title | The Eisenstein ideal with squarefree level |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T17%3A29%3A38IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_arxiv&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Eisenstein%20ideal%20with%20squarefree%20level&rft.jtitle=arXiv.org&rft.au=Wake,%20Preston&rft.date=2021-01-19&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.1804.06400&rft_dat=%3Cproquest_arxiv%3E2072208482%3C/proquest_arxiv%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2072208482&rft_id=info:pmid/&rfr_iscdi=true |