Fargues-Rapoport conjecture for p-adic period domains in the non-basic case

Abstract

We prove the Fargues-Rapoport conjecture for p-adic period domains in the nonbasic case with minuscule cocharacter. More precisely, we give a group theoretical criterion for the cases when the admissible locus and weakly admissible locus coincide. ContentsIntroduction 1 Notations 2 1. Kottwitz set and G-bundles on the Fargues-Fontaine curve 3 2. Admissible locus and weakly admissible locus 9 3. Hodge-Newton-decomposability 13 4. The action of Jb on the modifications of G-bundles 18 5. Newton stratification and weakly admissible locus 23 References 24

On certain extensions of vector bundles in $p$-adic geometry

“…For example, a partial answer to this question obtained by the author and his collaborators in [1] leads to the work of Hansen [8] that describes precise closure relations among the Harder-Narasimhan strata on the stack of vector bundles on the Fargues-Fontaine curve. In addition, a general answer to this question can be used to describe the geometry of the p-adic flag variety and the B + dR -Grassmannian in terms of two natural stratifications, namely the Harder-Narasimhan stratification and the Newton stratification, in line with the work of many authors including Caraiani-Scholze [2], Chen-Fargues-Shen [4], Shen [20], Chen [3], Viehmann [21], and Nguyen-Viehmann [16].…”

Hodge–Newton filtration for $p$-divisible groups with ramified endomorphism structure

“…In this sense, the present work could have a natural application to the study of the generic fibre of Rapoport-Zink spaces with finite level structure (application which is in fact in the author's plans). Passing to infinite level structure, this could lead to further progress towards the Harris-Viehmann conjecture, comparing with the work of Gaisin and Imai [15] in this direction (especially in light of the methods elaborated by Chen, Fargues and Shen in [5], but see also [35] and [4], based on the theory of vector bundles over the Fargues-Fontaine curve). Let us mention, in addition, that the conclusions of this work can be interpreted in terms of p-adic Galois representations.…”