On period spaces for p-divisible groups

By U. Hartl. 2007

449 citations recorded by the source corpus.

In their book Rapoport and Zink constructed rigid analytic period spaces for Fontaine’s filtered isocrystals, and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. We determine the image of these period morphisms, thereby contributing to a question of Grothendieck. We give examples showing that only in rare cases the image is all of the Rapoport-Zink period space.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/618a22b319e13529a3acf7ebfc998339033843ae

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Citations in the corpus

Connected components of affine Deligne–Lusztig varieties in mixed characteristic (2013, methodology): “poport-Zink space M˘ = M˘(G,b,µ). These spaces are formal schemes locally formally of ﬁnite type over SpfOL with a natural action of the group J. For the precise deﬁnition of these spaces we refer to [RZ]. There exists a J-equivariant locally constant morphism on M˘ κM˘ : M˘(G,b,µ) →Hom(X∗ Qp(G),Z) ”
Affine Grassmannians and the geometric Satake in mixed characteristic (2014, methodology): “In this case, the moduli problem M̆n,h := M̆(G, b, μ) can be extended to the whole category NilpW , as in [RZ]: for every R ∈ NilpW , M̆n,h(R) classify the groupoid of pairs (X, ι), where X is a p-divisible group over SpecR, and ι : X0 ⊗k R/p → X ⊗R R/p is a quasi-isogeny.”
Moduli of p-divisible groups (2012, methodology): “a. Then Hartl, after handling the case of equal characteristic, [Har11], used Kedlaya’s theory of ϕ-modules over the Robba ring to construct an open subset Fℓa ⊂Fℓwa, called the admissible locus, cf. [Har08].2 Roughly, it is the locus where the universal ﬁltered ϕ- module over Fℓcomes from a Qp-loca”
On the classification of rank-two representations of quasiprojective fundamental groups (2007, background): “Aside from the restriction to the group SL(2), this is standard material [31] [32] [74] [77] [99] [102] [130], but it seems like a good idea to have a discussion which corresponds to our specific situation.”
Special cycles on unitary Shimura varieties II: global theory (2009, methodology): “This p-adic uniformization is essentially just spelling out the general method of [52] in the special case at hand.”
The Newton stratification on deformations of local G-shtukas (2008, methodology): “5 Deformation theory of local G-shtukas 17 6 Rapoport-Zink spaces for local G-shtukas and affine Deligne-Lusztig varieties 22”
The supersingular locus of the Shimura variety of GU(1,n−1) II (2008, methodology): “By [13] Corollary 3.”
Geometrization of the local Langlands correspondence: an overview (2016, methodology): “[23] M. Rapoport and T. Zink.”
Faltings heights of abelian varieties with complex multiplication (2015, background): “position 3.5.2. Suppose that Np is a Kp-stable Zp-lattice in an algebraic Qp-representation Nof TQp. Then the Γy-representation Λp,y[p−1] is crystalline. Proof. Thisis essentially due to Rapoport-Zink[RZ96]. We give some details of the proof. Consider the map (3.5.1) Γy↪ I ab q Ð→ O≃ × E,q ↪ TE(Qp),”