Construction of a Rapoport–Zink space for
GU(1,1) in the ramified 2-adic case

Kirch, Daniel

doi:10.2140/pjm.2018.293.341

Cited by 2 publications

(4 citation statements)

References 18 publications

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“…Therefore, by Drinfeld's local theorem [9], the right hand side of (1.3.3) has an interpretation in terms of the Drinfeld halfplane Ω F . This is the main result of [17], for which we give a new proof, after it was already reproved by Kirch [14]. Theorem 1.3.1 follows.…”

Section: It Induces An Equivalence Of Categoriesmentioning

confidence: 68%

“…We also prove a refinement concerning descent data. The original proof was already simplified by Kirch [14], but the argument here is different and is based on the theory of displays. 5.1.…”

Section: The Alternative Moduli Problem Revisitedmentioning

confidence: 99%

“…It can also be characterized in terms of the moduli problem N , cf. [14]: it is a triple (X, ι, λ) consisting of a p-divisible strict formal O F -module X over κ F , with an action ι of O K satisfying the Kottwitz condition (5.2.3), and a perfect relative polarization λ such that the special automorphism group is isomorphic to SL 2 (F ), comp. [14, Prop.…”

Section: 2mentioning

confidence: 99%

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On the p-adic uniformization of unitary Shimura curves

Kudla¹,

Rapoport²,

Zink³

2020

Preprint

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We prove p-adic uniformization for Shimura curves attached to the group of unitary similitudes of certain binary skew hermitian spaces V with respect to an arbitrary CM field K with maximal totally real subfield F . For a place v|p of F that is not split in K and for which Vv is anisotropic, let ν be an extension of v to the reflex field E. We define an integral model of the corresponding Shimura curve over Spec O E,(ν) by means of a moduli problem for abelian schemes with suitable polarization and level structure prime to p. The formulation of the moduli problem involves a Kottwitz condition, an Eisenstein condition, and an adjusted invariant. The first two conditions are conditions on the Lie algebra of the abelian varieties; the last condition is a condition on the Riemann form of the polarization. The uniformization of the formal completion of this model along its special fiber is given in terms of the formal Drinfeld upper half plane Ω Fv for Fv. The proof relies on the construction of the contracting functor which relates a relative Rapoport-Zink space for strict formal O Fv -modules with a Rapoport-Zink space of p-divisible groups which arise from the moduli problem, where the O Fv -action is usually not strict when Fv = Qp. Our main tool is the theory of displays, in particular the Ahsendorf functor.

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Section: It Induces An Equivalence Of Categoriesmentioning

confidence: 68%

Section: The Alternative Moduli Problem Revisitedmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

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On the p-adic uniformization of unitary Shimura curves

Kudla¹,

Rapoport²,

Zink³

2020

Preprint

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“…Hom O k pX 0 , Xqr1{ps Ñ Hom O k pX 0ˆS S, XˆS Sqr1{ps 2 When p " 2 there is a thorough study of unitary Rapoport-Zink spaces of signature p1, 1q in the work of Kirch [Kir18], even when k{Qp is ramified.…”

Section: The Reduction Mapmentioning

confidence: 99%