Springer's theorem for tame quadratic forms over Henselian fields
A quadratic form over a Henselian-valued field of arbitrary residue characteristic is tame if it becomes hyperbolic over a tamely ramified extension. The Witt group of tame quadratic forms is shown to be canonically isomorphic to the Witt group of graded quadratic forms over the graded ring associat...
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | |
container_title | |
container_volume | |
creator | Elomary, Mohamed Abdou Tignol, Jean-Pierre |
description | A quadratic form over a Henselian-valued field of arbitrary residue
characteristic is tame if it becomes hyperbolic over a tamely ramified
extension. The Witt group of tame quadratic forms is shown to be canonically
isomorphic to the Witt group of graded quadratic forms over the graded ring
associated to the filtration defined by the valuation, hence also isomorphic to
a direct sum of copies of the Witt group of the residue field indexed by the
value group modulo 2. |
doi_str_mv | 10.48550/arxiv.1002.1153 |
format | Article |
fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1002_1153</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1002_1153</sourcerecordid><originalsourceid>FETCH-LOGICAL-a653-f0c7b469a52b05f29b16a4005b8572841ffed8d989a1156c79978bfea687d26f3</originalsourceid><addsrcrecordid>eNotjztPwzAURr0woJadCXnrlGA78WusKqBIlTrQPbqOr1tLeYAdKvj3NLTTJ53h0zmEPHJW1kZK9gzpJ55LzpgoOZfVPVl_fKY4HDGtMp1OOCbsaRgTnaBH-vUNPsEU2xn1mY5nTHSLQ8YuwkBDxM7nJbkL0GV8uO2CHF5fDpttsdu_vW_WuwKUrIrAWu1qZUEKx2QQ1nEFNWPSGamFqXkI6I23xsJFTLXaWm1cQFBGe6FCtSBP19v_hOZi3UP6beaUZk6p_gDjPEN2</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Springer's theorem for tame quadratic forms over Henselian fields</title><source>arXiv.org</source><creator>Elomary, Mohamed Abdou ; Tignol, Jean-Pierre</creator><creatorcontrib>Elomary, Mohamed Abdou ; Tignol, Jean-Pierre</creatorcontrib><description>A quadratic form over a Henselian-valued field of arbitrary residue
characteristic is tame if it becomes hyperbolic over a tamely ramified
extension. The Witt group of tame quadratic forms is shown to be canonically
isomorphic to the Witt group of graded quadratic forms over the graded ring
associated to the filtration defined by the valuation, hence also isomorphic to
a direct sum of copies of the Witt group of the residue field indexed by the
value group modulo 2.</description><identifier>DOI: 10.48550/arxiv.1002.1153</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - K-Theory and Homology</subject><creationdate>2010-02</creationdate><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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1002.1153$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1002.1153$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Elomary, Mohamed Abdou</creatorcontrib><creatorcontrib>Tignol, Jean-Pierre</creatorcontrib><title>Springer's theorem for tame quadratic forms over Henselian fields</title><description>A quadratic form over a Henselian-valued field of arbitrary residue
characteristic is tame if it becomes hyperbolic over a tamely ramified
extension. The Witt group of tame quadratic forms is shown to be canonically
isomorphic to the Witt group of graded quadratic forms over the graded ring
associated to the filtration defined by the valuation, hence also isomorphic to
a direct sum of copies of the Witt group of the residue field indexed by the
value group modulo 2.</description><subject>Mathematics - Algebraic Geometry</subject><subject>Mathematics - K-Theory and Homology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjztPwzAURr0woJadCXnrlGA78WusKqBIlTrQPbqOr1tLeYAdKvj3NLTTJ53h0zmEPHJW1kZK9gzpJ55LzpgoOZfVPVl_fKY4HDGtMp1OOCbsaRgTnaBH-vUNPsEU2xn1mY5nTHSLQ8YuwkBDxM7nJbkL0GV8uO2CHF5fDpttsdu_vW_WuwKUrIrAWu1qZUEKx2QQ1nEFNWPSGamFqXkI6I23xsJFTLXaWm1cQFBGe6FCtSBP19v_hOZi3UP6beaUZk6p_gDjPEN2</recordid><startdate>20100205</startdate><enddate>20100205</enddate><creator>Elomary, Mohamed Abdou</creator><creator>Tignol, Jean-Pierre</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20100205</creationdate><title>Springer's theorem for tame quadratic forms over Henselian fields</title><author>Elomary, Mohamed Abdou ; Tignol, Jean-Pierre</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a653-f0c7b469a52b05f29b16a4005b8572841ffed8d989a1156c79978bfea687d26f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Mathematics - Algebraic Geometry</topic><topic>Mathematics - K-Theory and Homology</topic><toplevel>online_resources</toplevel><creatorcontrib>Elomary, Mohamed Abdou</creatorcontrib><creatorcontrib>Tignol, Jean-Pierre</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Elomary, Mohamed Abdou</au><au>Tignol, Jean-Pierre</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Springer's theorem for tame quadratic forms over Henselian fields</atitle><date>2010-02-05</date><risdate>2010</risdate><abstract>A quadratic form over a Henselian-valued field of arbitrary residue
characteristic is tame if it becomes hyperbolic over a tamely ramified
extension. The Witt group of tame quadratic forms is shown to be canonically
isomorphic to the Witt group of graded quadratic forms over the graded ring
associated to the filtration defined by the valuation, hence also isomorphic to
a direct sum of copies of the Witt group of the residue field indexed by the
value group modulo 2.</abstract><doi>10.48550/arxiv.1002.1153</doi><oa>free_for_read</oa></addata></record> |
fulltext | fulltext_linktorsrc |
identifier | DOI: 10.48550/arxiv.1002.1153 |
ispartof | |
issn | |
language | eng |
recordid | cdi_arxiv_primary_1002_1153 |
source | arXiv.org |
subjects | Mathematics - Algebraic Geometry Mathematics - K-Theory and Homology |
title | Springer's theorem for tame quadratic forms over Henselian fields |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T07%3A36%3A26IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Springer's%20theorem%20for%20tame%20quadratic%20forms%20over%20Henselian%20fields&rft.au=Elomary,%20Mohamed%20Abdou&rft.date=2010-02-05&rft_id=info:doi/10.48550/arxiv.1002.1153&rft_dat=%3Carxiv_GOX%3E1002_1153%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |