Companion points and locally analytic socle conjecture for Steinberg case
In this paper, we will modify the Breuil-Hellmann-Schraen's (more generally, resp.,Breuil-Ding's) local model for the trianguline variety (resp.,Bernstein paraboline variety) to certain semistable (resp., potentially semistable) non-crystalline point with regular Hodge-Tate weights. Then w...
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| creator | He, Yiqin |
| description | In this paper, we will modify the Breuil-Hellmann-Schraen's (more generally,
resp.,Breuil-Ding's) local model for the trianguline variety (resp.,Bernstein
paraboline variety) to certain semistable (resp., potentially semistable)
non-crystalline point with regular Hodge-Tate weights. Then we deduce several
local-global compatibility results, including a classicality result, and the
existence of expected companion points on the (definite) eigenvariety and
locally analytic socle conjecture for certain semistable non-crystalline Galois
representations (in other words, the so-called Steinberg case), under some wild
hypothesis on on trianguline variety and the usual Taylor-Wiles assumptions. |
| doi_str_mv | 10.48550/arxiv.2401.13242 |
| format | Article |
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resp.,Breuil-Ding's) local model for the trianguline variety (resp.,Bernstein
paraboline variety) to certain semistable (resp., potentially semistable)
non-crystalline point with regular Hodge-Tate weights. Then we deduce several
local-global compatibility results, including a classicality result, and the
existence of expected companion points on the (definite) eigenvariety and
locally analytic socle conjecture for certain semistable non-crystalline Galois
representations (in other words, the so-called Steinberg case), under some wild
hypothesis on on trianguline variety and the usual Taylor-Wiles assumptions.</description><identifier>DOI: 10.48550/arxiv.2401.13242</identifier><language>eng</language><subject>Mathematics - Number Theory ; Mathematics - Representation Theory</subject><creationdate>2024-01</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2401.13242$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2401.13242$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>He, Yiqin</creatorcontrib><title>Companion points and locally analytic socle conjecture for Steinberg case</title><description>In this paper, we will modify the Breuil-Hellmann-Schraen's (more generally,
resp.,Breuil-Ding's) local model for the trianguline variety (resp.,Bernstein
paraboline variety) to certain semistable (resp., potentially semistable)
non-crystalline point with regular Hodge-Tate weights. Then we deduce several
local-global compatibility results, including a classicality result, and the
existence of expected companion points on the (definite) eigenvariety and
locally analytic socle conjecture for certain semistable non-crystalline Galois
representations (in other words, the so-called Steinberg case), under some wild
hypothesis on on trianguline variety and the usual Taylor-Wiles assumptions.</description><subject>Mathematics - Number Theory</subject><subject>Mathematics - Representation Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz7tOwzAYhmEvDKhwAUz4BhJ8tjuiiEOlSgztHvnwG7ly7cgJiNw9UJi-d_qkB6E7SnphpCQPtn2lz54JQnvKmWDXaDfU82RLqgVPNZVlxrYEnKu3Oa8_bfO6JI_n6jNgX8sJ_PLRAMfa8GGBVBy0d-ztDDfoKto8w-3_btDx-ek4vHb7t5fd8LjvrNKsiwKoUjFQQrgDSYzTQdNt4MJZL41hGkJQBoRUEgT1XJMgAzFGRUe1D3yD7v9uL5Zxauls2zr-msaLiX8DPylHaQ</recordid><startdate>20240124</startdate><enddate>20240124</enddate><creator>He, Yiqin</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240124</creationdate><title>Companion points and locally analytic socle conjecture for Steinberg case</title><author>He, Yiqin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-f4e166fd1003be508b7d719d34bac58827edd68e4565e41c370d5d0886fb17cd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Number Theory</topic><topic>Mathematics - Representation Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>He, Yiqin</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>He, Yiqin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Companion points and locally analytic socle conjecture for Steinberg case</atitle><date>2024-01-24</date><risdate>2024</risdate><abstract>In this paper, we will modify the Breuil-Hellmann-Schraen's (more generally,
resp.,Breuil-Ding's) local model for the trianguline variety (resp.,Bernstein
paraboline variety) to certain semistable (resp., potentially semistable)
non-crystalline point with regular Hodge-Tate weights. Then we deduce several
local-global compatibility results, including a classicality result, and the
existence of expected companion points on the (definite) eigenvariety and
locally analytic socle conjecture for certain semistable non-crystalline Galois
representations (in other words, the so-called Steinberg case), under some wild
hypothesis on on trianguline variety and the usual Taylor-Wiles assumptions.</abstract><doi>10.48550/arxiv.2401.13242</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Number Theory Mathematics - Representation Theory |
| title | Companion points and locally analytic socle conjecture for Steinberg case |
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