Topological flatness of local models for ramified unitary groups. II. The even dimensional case

Details Topological flatness of local models for ramified unitary groups. II. The even dimensional case Topological flatness of local models for ramified unitary groups. II. The even dimensional case

2011-10-28

arxiv.org/abs/1110.6424v1

Mathematics

Algebraic Geometry

83 pages

Scientific paper

Local models are schemes, defined in terms of linear-algebraic moduli problems, which give \'etale-local neighborhoods of integral models of certain p-adic PEL Shimura varieties defined by Rapoport and Zink. In the case of a unitary similitude group whose localization at Q_p is ramified, quasi-split GU_n, Pappas has observed that the original local models are typically not flat, and he and Rapoport have introduced new conditions to the original moduli problem which they conjecture to yield a flat scheme. In a previous paper we proved that their new local models are topologically flat when n is odd. In the present paper we prove topological flatness when n is even. Along the way, we characterize the mu-admissible set for certain cocharacters mu in types B and D, and we show that for these cocharacters admissibility can be characterized in a vertexwise way, confirming a conjecture of Pappas and Rapoport.

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