Fully Hodge-Newton decomposable Shimura varieties

Goertz, Ulrich; He, Xuhua; Nie, Sian

doi:10.48550/arxiv.1610.05381

Cited by 16 publications

(51 citation statements)

References 36 publications

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“…Recall that (cf. [17] Definition 2.1 and [3] 4.3) we have the notion of fully Hodge-Newton decomposability for the Kottwitz set B(G, µ) (or the pair (G, {µ})). This notion can be generalized to the sets B(G, 0, ν b µ −1 ) and B(J b , 0, ν b −1 µ).…”

Section: Fully Hodge-newton Decomposable Casementioning

confidence: 99%

“…There are some further (conjectural) equivalences for the fully Hodge-Newton decomposable condition (1). For example, we refer the reader to (1) [3] Conjecture 7.2 (in terms of fundamental domains of p-adic period domains and local Shimura varieties), (2) [17] Theorem 2.3 (in terms of the geometry of affine Deligne-Lusztig varieties).…”

Section: Fully Hodge-newton Decomposable Casementioning

confidence: 99%

“…First, we have Remark 6.1. By the classification of fully Hodge-Newton decomposable pairs in [17] Theorem 2.5, a fully Hodge-Newton decomposable pair (G, {µ}) with µ non minuscule can only be of the following form: after passage to the adjoint group over Qp , exactly one simple factor (G i , {µ i }) of (G ad Qp , {µ}) has non central µ i , in which case its associated triple (W a , µ, σ) is…”

Section: Non Minuscule Cocharactersmentioning

confidence: 99%

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Harder-Narasimhan strata and $p$-adic period domains

Shen

2019

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We revisit the Harder-Narasimhan stratification on a minuscule p-adic flag variety, by the theory of modifications of G-bundles on the Fargues-Fontaine curve. We compare the Harder-Narasimhan strata with the Newton strata introduced by Caraiani-Scholze. As a consequence, we get further equivalent conditions in terms of p-adic Hodge-Tate period domains for fully Hodge-Newton decomposable pairs. We also discuss the non minuscule cocharacter case by considering the associated B + dRaffine Schubert varieties. Applying Hodge-Tate period maps, our constructions give applications to p-adic geometry of Shimura varieties and their local analogues. Contents 1. Introduction 1 2. Modifications of G-bundles on the Fargues-Fontaine curve 5 3. Newton strata and Harder-Narasimhan strata on p-adic flag varieties 12 4. The twin towers principle and dualities for Newton and HN stratifications 17 5. Fully Hodge-Newton decomposable case 22 6. Non minuscule cocharacters 23 7. Application to moduli of local G-Shtukas 30 8. Application to Shimura varieties 31 References 32

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Section: Fully Hodge-newton Decomposable Casementioning

confidence: 99%

Section: Fully Hodge-newton Decomposable Casementioning

confidence: 99%

Section: Non Minuscule Cocharactersmentioning

confidence: 99%

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Harder-Narasimhan strata and $p$-adic period domains

Shen

2019

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“…Here the fully Hodge-Newton-decomposability condition is purely group theoretic. Görtz, He and Nie classified all the fully Hodge-Newton decomposable pairs and give more equivalent conditions of fully Hodge-Newton decomposability in their article [18]. When G is a general linear group, the triple (G, µ, b) is Hodge-Newton-indecomposable if all the breakpoints of the Newton polygon defined by b do not touch the Hodge polygon defined by µ.…”

Section: Introductionmentioning

confidence: 99%

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

Chen¹

2020

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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

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“…[36], [37]), and for the case where (G, µ) is fully Hodge-Newton decomposable (cf. [8]), see [18], [20], [41], [34], [39], [32], [12], [13], [6], [24], [25], [33] and so on for the precise descriptions and their applications in arithmetic geometry.…”

Section: Introductionmentioning

confidence: 99%