On a conjecture of Kottwitz and Rapoport

By Qendrim R. Gashi. 2008

60 citations recorded by the source corpus.

We prove a conjecture of Kottwitz and Rapoport which implies a converse to Mazur's Inequality for all split and quasi-split (connected) reductive groups. These results are related to the non-emptiness of certain affine Deligne-Lusztig varieties.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2aa011eece8204fabdd4e813ace0a0457ec628c1

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In Geometry and Topology

1. Xuhua He
2. E. Viehmann
3. Michael Rapoport
4. U. Hartl
5. Xinwen Zhu
6. Georgios Pappas
7. Peter Scholze
8. Thomas J. Haines

In Mathematical Physics

1. Xuhua He
2. E. Viehmann
3. Michael Rapoport
4. U. Hartl
5. Xinwen Zhu
6. Georgios Pappas
7. Peter Scholze
8. Thomas J. Haines

Citations in the corpus

• Kottwitz-Rapoport conjecture on unions of affine Deligne-Lusztig varieties (2014, methodology): “References [1] Q. Gashi, On a conjecture of Kottwitz and Rapoport, Ann.”
• GEOMETRIC AND HOMOLOGICAL PROPERTIES OF AFFINE DELIGNE-LUSZTIG VARIETIES (2012, methodology): “Following [5], we define a partial order (cid:22) J on Y + J as follows.”
• Ekedahl–Oort and Newton strata for Shimura varieties of PEL type (2010, unknown): “atum D. Let Γµ be the stabilizer of µin Γ and set µ¯ := [Γ : Γµ]−1 X τ∈Γ/Γµ τ(µ) ∈ (X∗(T) ⊗Q)Γ dom. Then by the work of Rapoport and Richartz [RR], Kottwitz and Rapoport [KR], Lucarelli [L] and Gashi [Ga], we have (7.6) B(G,µ) = {b∈ B(G) ; ν(b) ≤ µ,κ¯ (b) = µ♭ }. This is a finite set. The same argume”
• Connected components of affine Deligne–Lusztig varieties in mixed characteristic (2013, unknown): “e set Xµ(b) is non-empty if and only if κG(b) = [µ] in π1(G)Γ,and µ¯ −νdom is a linear combination of positive coroots with non-negative rational coefficients - see [KR], [Wi], [GHKR], Prop. 5.6.1, and [Ga]. We denote by B(G,µ) the set of σ-conjugacy classes [b] ∈B(G) satisfying these conditions, and ”
• Towards a theory of local Shimura varieties (2014, background): “ne Deligne-Lusztig variety associated to (G,b,{µ},G), cf. [79]. The question of when an affine Deligne-Lusztig variety is non-empty has been much studied but is still open in the most general case, cf. [21, 26, 28, 35, 79]. In any case, having fixed the element b ∈[b], simple rational RZ data define the”
• The \mu-ordinary locus for Shimura varieties of Hodge type (2013, unknown): “ ∨ |α∨ ∈Φ∨i) hσi. Definition 5.6. Let B(G,µ) := b∈B(G) |κG(b) = µ♮, νG(b) µ¯ . We endow B(G,µ) ⊂B(G) with the induced partial order . By work of Kottwitz-Rapoport ([KR]), Lucarelli ([Lu]) and Gashi ([Ga]) we knowthat B(G,µ) isexactlythe imageofthedouble cosetG(W(k))µ(p)G(W(k)) in B(G) (for any algebr”
• The Newton stratification on deformations of local G-shtukas (2008, background): “There is a criterion for XmðbÞ to be non-empty, see [34] and [14].”