Bruhat–Tits theory from Berkovich’s point of view. Analytic filtrations
[Point de vue de Berkovich sur l’immeuble et filtrations]
Mayeux, Arnaud1
1 Université Clermont-Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand (France)
Annales Henri Lebesgue, Tome 5 (2022), pp. 813-839.

Nous définissons des groupes affinoïdes, dans l’analytifié d’un groupe réductif connexe, étroitement liés aux filtrations de Moy–Prasad. Ils sont paramétrés par un cône, dont la base est l’immeuble de Bruhat–Tits et dont le sommet est l’élément neutre, grâce aux notions de bord de Shilov et d’enveloppe convexe holomorphe.

We define filtrations by affinoid groups, in the Berkovich analytification of a connected reductive group, related to Moy–Prasad filtrations. They are parametrized by a cone, whose basis is the Bruhat–Tits building and whose vertex is the neutral element, via the notions of Shilov boundary and holomorphically convex envelope.

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DOI : 10.5802/ahl.137
Classification : 20G25, 20E42, 14G22
Mots clés : Berkovich spaces, Bruhat–Tits buildings, Moy–Prasad filtrations
Mayeux, Arnaud 1

1 Université Clermont-Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand (France) 
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Mayeux, Arnaud. Bruhat–Tits theory from Berkovich’s point of view. Analytic filtrations. Annales Henri Lebesgue, Tome 5 (2022), pp. 813-839. doi : 10.5802/ahl.137. http://archive.numdam.org/articles/10.5802/ahl.137/

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