Parametrization of tamely ramified maximal tori using bounded subgroups
Identifieur interne : 000E93 ( Istex/Corpus ); précédent : 000E92; suivant : 000E94Parametrization of tamely ramified maximal tori using bounded subgroups
Auteurs : François CourtèsSource :
- Annali di Matematica Pura ed Applicata [ 0373-3114 ] ; 2009-01-01.
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Abstract
Abstract: Let $$\underline{G}$$ be a reductive group defined over a local complete field F with discrete valuation, and split over some unramified extension of F, and let G be its group of F-points. In this paper, we define a class of abelian “torus-like” subgroups in nonreductive groups, called pseudo-tori, which generalizes the notion of torus, and we establish a correspondence between conjugacy classes of tamely ramified maximal tori of G and association classes of maximal pseudo-tori of the quotients of parahorics of G by their second congruence subgroup, viewed as groups of k-points of algebraic groups defined over the residual field k of F.
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DOI: 10.1007/s10231-007-0064-z
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In this paper, we define a class of abelian “torus-like” subgroups in nonreductive groups, called pseudo-tori, which generalizes the notion of torus, and we establish a correspondence between conjugacy classes of tamely ramified maximal tori of G and association classes of maximal pseudo-tori of the quotients of parahorics of G by their second congruence subgroup, viewed as groups of k-points of algebraic groups defined over the residual field k of F.</div></front></TEI><istex><corpusName>springer-journals</corpusName><author><json:item><name>François Courtès</name><affiliations><json:string>Département de Mathématiques, CNRS Université de Poitiers, UMR 6086 du CNRS, Téléport 2, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex, France</json:string><json:string>E-mail: courtes@math.univ-poitiers.fr</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Reductive groups over local fields</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Maximal tori</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Bounded subgroups</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Linear algebraic groups over residual fields</value></json:item></subject><articleId><json:string>64</json:string><json:string>s10231-007-0064-z</json:string></articleId><arkIstex>ark:/67375/VQC-61RCH0PR-7</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: Let $$\underline{G}$$ be a reductive group defined over a local complete field F with discrete valuation, and split over some unramified extension of F, and let G be its group of F-points. 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discrete valuation, and split over some unramified extension of <Emphasis Type="Italic">F</Emphasis>, and let <Emphasis Type="Italic">G</Emphasis> be its group of <Emphasis Type="Italic">F</Emphasis>-points. In this paper, we define a class of abelian “torus-like” subgroups in nonreductive groups, called pseudo-tori, which generalizes the notion of torus, and we establish a correspondence between conjugacy classes of tamely ramified maximal tori of <Emphasis Type="Italic">G</Emphasis> and association classes of maximal pseudo-tori of the quotients of parahorics of <Emphasis Type="Italic">G</Emphasis> by their second congruence subgroup, viewed as groups of <Emphasis Type="Italic">k</Emphasis>-points of algebraic groups defined over the residual field <Emphasis Type="Italic">k</Emphasis> of <Emphasis Type="Italic">F</Emphasis>.</Para></Abstract><KeywordGroup Language="En"><Heading>Keywords</Heading><Keyword>Reductive groups over local fields</Keyword><Keyword>Maximal tori</Keyword><Keyword>Bounded subgroups</Keyword><Keyword>Linear algebraic groups over residual fields</Keyword></KeywordGroup><KeywordGroup Language="--" OutputMedium="All"><Heading>Mathematics Subject Classification (2000)</Heading><Keyword>22E20</Keyword><Keyword>20G15</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Parametrization of tamely ramified maximal tori using bounded subgroups</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Parametrization of tamely ramified maximal tori using bounded subgroups</title></titleInfo><name type="personal" displayLabel="corresp"><namePart type="given">François</namePart><namePart type="family">Courtès</namePart><affiliation>Département de Mathématiques, CNRS Université de Poitiers, UMR 6086 du CNRS, Téléport 2, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex, France</affiliation><affiliation>E-mail: courtes@math.univ-poitiers.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">Berlin/Heidelberg</placeTerm></place><dateCreated encoding="w3cdtf">2007-06-05</dateCreated><dateIssued encoding="w3cdtf">2009-01-01</dateIssued><dateIssued encoding="w3cdtf">2007</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: Let $$\underline{G}$$ be a reductive group defined over a local complete field F with discrete valuation, and split over some unramified extension of F, and let G be its group of F-points. 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