Ihara’s Lemma for Shimura curves over totally real fields via patching
We prove Ihara’s lemma for the mod l cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois representation. This was proved by Diamond and Taylor, for Shimura curves over Q , under various assumptions on l . Our method...
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| Veröffentlicht in: | Mathematische annalen 2021-02, Vol.379 (1-2), p.187-234 |
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| container_title | Mathematische annalen |
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| creator | Manning, Jeffrey Shotton, Jack |
| description | We prove Ihara’s lemma for the mod
l
cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois representation. This was proved by Diamond and Taylor, for Shimura curves over
Q
, under various assumptions on
l
. Our method is totally different and can avoid these assumptions, at the cost of imposing the large image hypothesis. It uses the Taylor–Wiles method, as improved by Diamond and Kisin, and the geometry of integral models of Shimura curves at an auxiliary prime. |
| doi_str_mv | 10.1007/s00208-020-02048-8 |
| format | Article |
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l
cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois representation. This was proved by Diamond and Taylor, for Shimura curves over
Q
, under various assumptions on
l
. Our method is totally different and can avoid these assumptions, at the cost of imposing the large image hypothesis. It uses the Taylor–Wiles method, as improved by Diamond and Kisin, and the geometry of integral models of Shimura curves at an auxiliary prime.</description><identifier>ISSN: 0025-5831</identifier><identifier>EISSN: 1432-1807</identifier><identifier>DOI: 10.1007/s00208-020-02048-8</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Curves ; Diamonds ; Homology ; Hypotheses ; Mathematics ; Mathematics and Statistics ; Patching</subject><ispartof>Mathematische annalen, 2021-02, Vol.379 (1-2), p.187-234</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-9fcd38406915259d205302330ce3f10ee9e1d75abdac2fc060575ce3829b26563</citedby><cites>FETCH-LOGICAL-c363t-9fcd38406915259d205302330ce3f10ee9e1d75abdac2fc060575ce3829b26563</cites><orcidid>0000-0002-3464-8791</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00208-020-02048-8$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00208-020-02048-8$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,778,782,27907,27908,41471,42540,51302</link.rule.ids></links><search><creatorcontrib>Manning, Jeffrey</creatorcontrib><creatorcontrib>Shotton, Jack</creatorcontrib><title>Ihara’s Lemma for Shimura curves over totally real fields via patching</title><title>Mathematische annalen</title><addtitle>Math. Ann</addtitle><description>We prove Ihara’s lemma for the mod
l
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Q
, under various assumptions on
l
. Our method is totally different and can avoid these assumptions, at the cost of imposing the large image hypothesis. It uses the Taylor–Wiles method, as improved by Diamond and Kisin, and the geometry of integral models of Shimura curves at an auxiliary prime.</description><subject>Curves</subject><subject>Diamonds</subject><subject>Homology</subject><subject>Hypotheses</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Patching</subject><issn>0025-5831</issn><issn>1432-1807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9ULtOwzAUtRBIlMIPMFliNlzbceKMqAJaqRIDMFuuYzep8ih2Eqkbv8Hv8SW4BImN4Z47nJd0ELqmcEsBsrsAwECSCMdLJJEnaEYTzgiVkJ2iWeQFEZLTc3QRwg4AOICYoeWq1F5_fXwGvLZNo7HrPH4pq2bwGpvBjzbgbrQe912v6_qAvdU1dpWti4DHSuO97k1ZtdtLdOZ0HezV75-jt8eH18WSrJ-fVov7NTE85T3JnSm4TCDNqWAiLxgIDoxzMJY7CtbmlhaZ0JtCG-YMpCAyETnJ8g1LRcrn6GbK3fvufbChV7tu8G2sVCyRqYh5CYsqNqmM70Lw1qm9rxrtD4qCOi6mpsVUBPWzmJLRxCdTiOJ2a_1f9D-ub_kLbbU</recordid><startdate>20210201</startdate><enddate>20210201</enddate><creator>Manning, Jeffrey</creator><creator>Shotton, Jack</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-3464-8791</orcidid></search><sort><creationdate>20210201</creationdate><title>Ihara’s Lemma for Shimura curves over totally real fields via patching</title><author>Manning, Jeffrey ; Shotton, Jack</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-9fcd38406915259d205302330ce3f10ee9e1d75abdac2fc060575ce3829b26563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Curves</topic><topic>Diamonds</topic><topic>Homology</topic><topic>Hypotheses</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Patching</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Manning, Jeffrey</creatorcontrib><creatorcontrib>Shotton, Jack</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Mathematische annalen</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Manning, Jeffrey</au><au>Shotton, Jack</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Ihara’s Lemma for Shimura curves over totally real fields via patching</atitle><jtitle>Mathematische annalen</jtitle><stitle>Math. Ann</stitle><date>2021-02-01</date><risdate>2021</risdate><volume>379</volume><issue>1-2</issue><spage>187</spage><epage>234</epage><pages>187-234</pages><issn>0025-5831</issn><eissn>1432-1807</eissn><abstract>We prove Ihara’s lemma for the mod
l
cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois representation. This was proved by Diamond and Taylor, for Shimura curves over
Q
, under various assumptions on
l
. Our method is totally different and can avoid these assumptions, at the cost of imposing the large image hypothesis. It uses the Taylor–Wiles method, as improved by Diamond and Kisin, and the geometry of integral models of Shimura curves at an auxiliary prime.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00208-020-02048-8</doi><tpages>48</tpages><orcidid>https://orcid.org/0000-0002-3464-8791</orcidid><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Curves Diamonds Homology Hypotheses Mathematics Mathematics and Statistics Patching |
| title | Ihara’s Lemma for Shimura curves over totally real fields via patching |
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