Congruences of Galois representations attached to effective \(A\)-motives over global function fields

This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be i...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2023-07
Main Author: Okumura, Yoshiaki
Format: Article
Language:English
Subjects:
Congruences
Criteria
Number theory
Representations
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Okumura, Yoshiaki
description This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of \(K\). This is a function field analog of Ozeki-Taguchi's criterion for \(\ell\)-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective \(A\)-motives with some constrained.
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2652727659</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2652727659</sourcerecordid><originalsourceid>FETCH-proquest_journals_26527276593</originalsourceid><addsrcrecordid>eNqNi00KwjAQRoMgWNQ7DLjRRaEmttWlFH8O4FIosU60EjM1k_b8tuABXD0-3vdGIpJKrePtRsqJmDO_kiSRWS7TVEUCC3IP36KrkIEMnLSlmsFj45HRBR1qcgw6BF098Q6BAI3BKtQdwnW5v67iNw2jrzv08LB00xZM66qhBFOjvfNMjI22jPMfp2JxPFyKc9x4-rTIoXxR612vSpmlMpd5lu7Uf68vpI1HIA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2652727659</pqid></control><display><type>article</type><title>Congruences of Galois representations attached to effective \(A\)-motives over global function fields</title><source>Publicly Available Content Database</source><creator>Okumura, Yoshiaki</creator><creatorcontrib>Okumura, Yoshiaki</creatorcontrib><description>This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of \(K\). This is a function field analog of Ozeki-Taguchi's criterion for \(\ell\)-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective \(A\)-motives with some constrained.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Congruences ; Criteria ; Number theory ; Representations</subject><ispartof>arXiv.org, 2023-07</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><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2652727659?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Okumura, Yoshiaki</creatorcontrib><title>Congruences of Galois representations attached to effective \(A\)-motives over global function fields</title><title>arXiv.org</title><description>This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of \(K\). This is a function field analog of Ozeki-Taguchi's criterion for \(\ell\)-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective \(A\)-motives with some constrained.</description><subject>Congruences</subject><subject>Criteria</subject><subject>Number theory</subject><subject>Representations</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNi00KwjAQRoMgWNQ7DLjRRaEmttWlFH8O4FIosU60EjM1k_b8tuABXD0-3vdGIpJKrePtRsqJmDO_kiSRWS7TVEUCC3IP36KrkIEMnLSlmsFj45HRBR1qcgw6BF098Q6BAI3BKtQdwnW5v67iNw2jrzv08LB00xZM66qhBFOjvfNMjI22jPMfp2JxPFyKc9x4-rTIoXxR612vSpmlMpd5lu7Uf68vpI1HIA</recordid><startdate>20230704</startdate><enddate>20230704</enddate><creator>Okumura, Yoshiaki</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></search><sort><creationdate>20230704</creationdate><title>Congruences of Galois representations attached to effective \(A\)-motives over global function fields</title><author>Okumura, Yoshiaki</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_26527276593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Congruences</topic><topic>Criteria</topic><topic>Number theory</topic><topic>Representations</topic><toplevel>online_resources</toplevel><creatorcontrib>Okumura, Yoshiaki</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</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></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Okumura, Yoshiaki</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Congruences of Galois representations attached to effective \(A\)-motives over global function fields</atitle><jtitle>arXiv.org</jtitle><date>2023-07-04</date><risdate>2023</risdate><eissn>2331-8422</eissn><abstract>This article investigates congruences of \(\mathfrak{p}\)-adic representations arising from effective \(A\)-motives defined over a global function field \(K\). We give a criterion for two congruent \(\mathfrak{p}\)-adic representations coming from strongly semi-stable effective \(A\)-motives to be isomorphic up to semi-simplification when restricted to decomposition groups of suitable places of \(K\). This is a function field analog of Ozeki-Taguchi's criterion for \(\ell\)-adic representations of number fields. Motivated by a non-existence conjecture on abelian varieties over number fields stated by Rasmussen and Tamagawa, we also show that there exist no strongly semi-stable effective \(A\)-motives with some constrained.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2023-07
issn 2331-8422
language eng
recordid cdi_proquest_journals_2652727659
source Publicly Available Content Database
subjects Congruences
Criteria
Number theory
Representations
title Congruences of Galois representations attached to effective \(A\)-motives over global function fields
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-29T10%3A35%3A16IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Congruences%20of%20Galois%20representations%20attached%20to%20effective%20%5C(A%5C)-motives%20over%20global%20function%20fields&rft.jtitle=arXiv.org&rft.au=Okumura,%20Yoshiaki&rft.date=2023-07-04&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2652727659%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_26527276593%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2652727659&rft_id=info:pmid/&rfr_iscdi=true