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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Mots clés : Berkovich spaces, Bruhat–Tits buildings, Moy–Prasad filtrations
@article{AHL_2022__5__813_0, author = {Mayeux, Arnaud}, title = {Bruhat{\textendash}Tits theory from {Berkovich{\textquoteright}s} point of view. {Analytic} filtrations}, journal = {Annales Henri Lebesgue}, pages = {813--839}, publisher = {\'ENS Rennes}, volume = {5}, year = {2022}, doi = {10.5802/ahl.137}, language = {en}, url = {http://www.numdam.org/articles/10.5802/ahl.137/} }
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://www.numdam.org/articles/10.5802/ahl.137/
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