Parametrization of tamely ramified maximal tori using bounded subgroups
Identifieur interne : 000954 ( Main/Exploration ); précédent : 000953; suivant : 000955Parametrization of tamely ramified maximal tori using bounded subgroups
Auteurs : François Courtès [France]Source :
- Annali di Matematica Pura ed Applicata [ 0373-3114 ] ; 2009-01-01.
English descriptors
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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.
Url:
DOI: 10.1007/s10231-007-0064-z
Affiliations:
- France
- Nouvelle-Aquitaine, Poitou-Charentes
- Futuroscope Chasseneuil, Poitiers
- Université de Poitiers
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