Local models for ramified unitary groups
نویسنده
چکیده
S′ −−−−→ Spec(OE) is cartesian. To qualify as a model, the scheme S′ should at least be flat over Spec(OE) and have only “good” singularities. In the PEL-case, S can be written as a moduli space of abelian varieties with polarization, an action by a semisimple Q-algebra and a K-level strucure where K ⊂ G(Af ) is an open and compact subgroup. If we fix a prime p , the investigation of a model S′ at p can be reduced to the investigation of the associated “local model” M , introduced in [9] – at least if K = K.Kp where K p ⊂ G(Apf ) 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 lying over p and denote by R the completion of (OE)p . Then the local model M is a closed subscheme of a Grassmannian, defined over Spec(R) . Locally for the étale topology M coincides with S′ ⊗OE R . Hence S ′ is flat if and only if the local model is and both schemes have the same singularities. We are going to study local models Mr,s of Shimura varieties where G is a
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تاریخ انتشار 2007