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.Contents 24 7. Asymptotic geometry of the admissible locus 28 References 30
We prove that, for a p-divisible group with additional structures over a complete valuation ring of rank one OK with mixed characteristic (0, p), if the Newton polygon and the Hodge polygon of its special fiber possess a non trivial contact point, which is a break point for the Newton polygon, then it admits a "Hodge-Newton filtration" over OK . The proof is based on the theories of Harder-Narasimhan filtration of finite flat group schemes and admissible filtered isocrystals. We then apply this result to the study of some larger class of Rapoport-Zink spaces and Shimura varieties than those in [27], and confirm some new cases of Harris's conjecture 5.2 in [18].
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