On the arithmetic moduli schemes of PEL Shimura varieties

By Georgios Pappas. 2000

85 citations recorded by the source corpus.

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Citations in the corpus

Local models in the ramified case, II: Splitting models (2002, methodology): “f both papers is to come to grips with the local models of Shimura varieties in the case where the group Gdeﬁning the Shimura variety splits over a ramiﬁed extension of Qp. As was ﬁrst pointed out in [P], in this case the “naive” local models of [RZ] are not ﬂat in general. One wants to deﬁne closed”
Introduction to Shimura Varieties with Bad Reduction of Parahoric Type (2004, methodology): “ic to the (polarized) multichain {Λ⊗Z p OS}. Moreover, the functor Isom T→Isom({M Λ ⊗OT},{Λ⊗OT}), is represented by a smooth aﬃne scheme over S. The analogous statements hold for any Zp-scheme S, see [P]. In particular for such Swe have a smooth aﬃne group scheme Gover Sgiven by G(T) = Aut({Λ⊗OT}), ”
Local models in the ramified case. III Unitary groups (2007, background): “In this case, it was shown in [23] that the models proposed in [29] are not flat in general.”
On the coherence conjecture of Pappas and Rapoport (2010, background): “-type Shimura varieties associated to unramiﬁed unitary groups and symplectic groups (some special cases were obtained in earlier works [CN, dJ, DP]). On the other hand, a discovery of G. Pappas (cf. [Pa]) showed that the originally deﬁned integral models in [RZ] are usually not ﬂat when the groups ”
Local models of Shimura varieties, I. Geometry and combinatorics (2010, methodology): “The paper [75] of Pappas pointed to the fact that naive local models are not always flat.”
Integral models of Shimura varieties with parahoric level structure (2015, background): “It had been conjectured by Rapoport [60, §6,7] (see also [53]), that ShK◦(G,X) admits an integral model SK◦(G,X), whose singularities are controlled by a “local model”, M G,X , with an explicit group theoretic description.”
Local models of Shimura varieties and a conjecture of Kottwitz (2011, methodology): “Indeed, then the corresponding integral models are often not flat ([44]).”
The Geometric Satake Correspondence for Ramified Groups (2011, background): “Indeed, as shown in [21, 23], when n = r + s is odd and (r, s) = (n− 1, 1), for the special parahoric Kp of G(Qp) with reductive quotient GOn, ShKp is not even semi-stable.”
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.”
Integral canonical models for Spin Shimura varieties (2012, methodology): “→Snv K (G,X) by constructing a ‘reﬁned’ local model Mref G that resolves the singularities of M loc G . This is essentially an instance of the notion of a ‘linear modiﬁcation’ introduced by Pappas in [Pap00]. We have to work a bit harder to show that this model is actually canonical. In particular, ”
On the flatness of local models for the symplectic group (2000, result): “ ﬁnite unramiﬁed extension of Qp. In the case where the underlying group does not split over an unramiﬁed extension, the ﬂatness conjecture is not true as it stands, as has been pointed out by Pappas [P]; see also [PR] for ideas on how to proceed in this case. Several special cases of our main theor”