Explicit non-Gorenstein R=T via rank bounds II: Computational aspects

Explicit non-Gorenstein R=T via rank bounds II: Computational aspects

This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. W...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:arXiv.org 2023-03
Hauptverfasser: Hsu, Catherine, Wake, Preston, Wang-Erickson, Carl
Format: Artikel
Sprache:eng
Schlagworte:
Criteria
Deformation
Mathematics - Number Theory
Number theory
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 Hsu, Catherine
Wake, Preston
Wang-Erickson, Carl
description This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. We adapt a technique developed by Sharifi to compute number fields with twisted-Heisenberg Galois group and prescribed ramification, and compute the splitting behavior of primes in these extensions.
doi_str_mv 10.48550/arxiv.2209.00556
format Article
fullrecord <record><control><sourceid>proquest_arxiv</sourceid><recordid>TN_cdi_arxiv_primary_2209_00556</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2709195694</sourcerecordid><originalsourceid>FETCH-LOGICAL-a956-db2489900bd4f313453152faab6e06150e6e03f1a39addf6e12b05681d8fb9ba3</originalsourceid><addsrcrecordid>eNotj0FLwzAYhoMgOOZ-gCcDnlu_JE3WCB5kzDkYCLJ7-bKmkNklNWnH_Pd2m6f38vDyPIQ8MMiLUkp4xnhyx5xz0DmAlOqGTLgQLCsLzu_ILKU9AHA151KKCVkuT13rdq6nPvhsFaL1qbfO06_XLT06pBH9NzVh8HWi6_ULXYRDN_TYu-CxpZg6u-vTPbltsE129r9Tsn1fbhcf2eZztV68bTLUUmW14UWpNYCpi0YwUUjBJG8QjbKgmAQ7rmgYCo113SjLuAGpSlaXjdEGxZQ8Xm8vjVUX3QHjb3VurS6tI_F0JboYfgab-mofhjiaporPQbNRQxfiD25vViM</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2709195694</pqid></control><display><type>article</type><title>Explicit non-Gorenstein R=T via rank bounds II: Computational aspects</title><source>arXiv.org</source><source>Free E- Journals</source><creator>Hsu, Catherine ; Wake, Preston ; Wang-Erickson, Carl</creator><creatorcontrib>Hsu, Catherine ; Wake, Preston ; Wang-Erickson, Carl</creatorcontrib><description>This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. We adapt a technique developed by Sharifi to compute number fields with twisted-Heisenberg Galois group and prescribed ramification, and compute the splitting behavior of primes in these extensions.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2209.00556</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Criteria ; Deformation ; Mathematics - Number Theory ; Number theory</subject><ispartof>arXiv.org, 2023-03</ispartof><rights>2023. 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/10.1007/s40993-022-00401-1$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2209.00556$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Hsu, Catherine</creatorcontrib><creatorcontrib>Wake, Preston</creatorcontrib><creatorcontrib>Wang-Erickson, Carl</creatorcontrib><title>Explicit non-Gorenstein R=T via rank bounds II: Computational aspects</title><title>arXiv.org</title><description>This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. We adapt a technique developed by Sharifi to compute number fields with twisted-Heisenberg Galois group and prescribed ramification, and compute the splitting behavior of primes in these extensions.</description><subject>Criteria</subject><subject>Deformation</subject><subject>Mathematics - Number Theory</subject><subject>Number theory</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</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>eNotj0FLwzAYhoMgOOZ-gCcDnlu_JE3WCB5kzDkYCLJ7-bKmkNklNWnH_Pd2m6f38vDyPIQ8MMiLUkp4xnhyx5xz0DmAlOqGTLgQLCsLzu_ILKU9AHA151KKCVkuT13rdq6nPvhsFaL1qbfO06_XLT06pBH9NzVh8HWi6_ULXYRDN_TYu-CxpZg6u-vTPbltsE129r9Tsn1fbhcf2eZztV68bTLUUmW14UWpNYCpi0YwUUjBJG8QjbKgmAQ7rmgYCo113SjLuAGpSlaXjdEGxZQ8Xm8vjVUX3QHjb3VurS6tI_F0JboYfgab-mofhjiaporPQbNRQxfiD25vViM</recordid><startdate>20230316</startdate><enddate>20230316</enddate><creator>Hsu, Catherine</creator><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>20230316</creationdate><title>Explicit non-Gorenstein R=T via rank bounds II: Computational aspects</title><author>Hsu, Catherine ; Wake, Preston ; Wang-Erickson, Carl</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a956-db2489900bd4f313453152faab6e06150e6e03f1a39addf6e12b05681d8fb9ba3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Criteria</topic><topic>Deformation</topic><topic>Mathematics - Number Theory</topic><topic>Number theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Hsu, Catherine</creatorcontrib><creatorcontrib>Wake, Preston</creatorcontrib><creatorcontrib>Wang-Erickson, Carl</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; 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>Publicly Available Content Database</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>Hsu, Catherine</au><au>Wake, Preston</au><au>Wang-Erickson, Carl</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Explicit non-Gorenstein R=T via rank bounds II: Computational aspects</atitle><jtitle>arXiv.org</jtitle><date>2023-03-16</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>This is the second in a pair of papers about residually reducible Galois deformation rings with non-optimal level. In the first paper, we proved a Galois-theoretic criterion for the deformation ring to be as small as possible. This paper focuses on the computations needed to verify this criterion. We adapt a technique developed by Sharifi to compute number fields with twisted-Heisenberg Galois group and prescribed ramification, and compute the splitting behavior of primes in these extensions.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2209.00556</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2023-03
issn 2331-8422
language eng
recordid cdi_arxiv_primary_2209_00556
source arXiv.org; Free E- Journals
subjects Criteria
Deformation
Mathematics - Number Theory
Number theory
title Explicit non-Gorenstein R=T via rank bounds II: Computational aspects
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-24T18%3A02%3A56IST&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=Explicit%20non-Gorenstein%20R=T%20via%20rank%20bounds%20II:%20Computational%20aspects&rft.jtitle=arXiv.org&rft.au=Hsu,%20Catherine&rft.date=2023-03-16&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.2209.00556&rft_dat=%3Cproquest_arxiv%3E2709195694%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=2709195694&rft_id=info:pmid/&rfr_iscdi=true