Local models for ramified unitary groups
Citations
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Cites methods from "Local models for ramified unitary g..."
...The blowup M̃ locG,{µ},L occurring in (ii) is described explicitly by Krämer in [Kr] in terms of a moduli problem analogous to the Demazure resolution of a Schubert variety in the Grassmannian....
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...Finally, we mention the papers by Gaitsgory [30], Haines and Ngô [42], Görtz [36], Haines [40, 41, 44], Krämer [57], Pappas and Zhu [82], Rostami [88], and Zhu [99] addressing the problem of determining the complex of nearby cycles for local models (Kottwitz conjecture)....
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...Finally, we mention the papers by Gaitsgory [Ga], Haines and Ngô [HN1], Görtz [Gö3], Haines [H1, H2, HP], and Krämer [Kr], addressing the problem of determining the complex of nearby cycles for local models (Kottwitz conjecture)....
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...The blowup M̃loc G,{μ},L occurring in (ii) is described explicitly by Krämer in [57] in terms of a moduli problem analogous to the Demazure resolution of a Schubert variety in the Grassmannian....
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Cites background from "Local models for ramified unitary g..."
...The stack M is only flat and regular after inverting disc(K0), but Pappas [37] and Krämer [19] have modified the moduli problem defining M in order to obtain a flat and regular moduli stack which agrees with M over OK0 [disc(K0) −1]....
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...It seems likely that the results of Lan’s thesis can be extended to give a compactification of the integral model of Pappas and Krämer, but the details have not been written down....
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...Thus one expects to obtain a class in the generalized arithmetic Chow group of Burgos-Gil–Kramer–Kühn [4, 5]....
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...stack M is only flat and regular after inverting disc(K0), but Pappas [37] and Krämer [19] have modified the moduli problem definingM in order to obtain a flat and regular moduli stack that agrees withM over OK0 [disc(K0)]....
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References
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"Local models for ramified unitary g..." refers background in this paper
...el strucure where K⊂G(Af) is an open and compact subgroup. If we fix a prime p, the investigation of a model S′ at pcan be reduced to the investigation of the associated “local model” M, introduced in [9] – at least if K= Kp.Kp where Kp ⊂G(Ap f) and Kp ⊂G(Qp) is a parahoric subgroup. In this work we will consider the case that Kp is a maximal parahoric subgroup of G(Qp). We further fix a prime p of OE ...
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...model is and both schemes have the same singularities. We are going to study local models Mr,s of Shimura varieties where Gis a 1 1 INTRODUCTION 2 reductive group over Q such that G⊗Q R = GU(r,s). In [9] it is conjectured that Mr,s is flat over the base R. This is true if pis unramified by the work of Go¨rtz [4], but an argument of Pappas shows that this is not true in general: Using the facts that the...
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243 citations
Additional excerpts
... point ythe alternating semisimple trace of Frobenius equals Trss(Frob q;RΨt(Ql)y) = z·(1 −q)+(|P(ΠΛ)(Fq)|−z) ·1 = z·(1 −q)+ qn −1 q−1 −z = qn −1 q−1 −z·q. There is an explicit formula for z(see e.g. [6], lemma 1.3.1): z= qn−1 −χqn 2 −1 +χqn 2 −1 q−1 ; with χ= 0 if nis odd and χ= 1 or −1 if nis even, depending on whether Fn q is hyperbolic with respect to v→ P v2 i or not. Combining these two results...
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94 citations
"Local models for ramified unitary g..." refers background or methods in this paper
...While the naive local model M cannot be flat over Spec(R) if |r − s| > 1 , Pappas conjectures in [7] that M loc is flat for every pair (r, s) ....
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...In [7], this was done by blowing up the singular locus....
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...In fact, Pappas is able to show the flatness of M loc r,s if (r, s) = (n− 1, 1) (see [7], theorem 4....
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...This proof is more or less a replication of Pappas’ proof in [7]....
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...Pappas conjectures in [7] that M loc = M if |r − s| ≤ 1 and is able to prove this in the case (r, s) = (2, 1) (see [7] 4....
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