On the structure of some $p$-adic period domains
Résumé
We study the geometry of the p-adic analogues of the complex analytic period spaces first introduced by Griffiths. More precisely, we prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group G over a p-adic field and a minuscule cocharacter µ of G, the weakly admissible locus coincides with the admissible one if and only if the Kottwitz set B(G, µ) is fully Hodge-Newton decomposable.
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