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arXiv · 1110.6424

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

Brian D. Smithling
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Abstract

Local models are schemes, defined in terms of linear-algebraic moduli problems, which give étale-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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Brian D. Smithling. 2011-10-28. Topological flatness of local models for ramified unitary groups. II. The even dimensional case. https://doi.org/10.1017/s1474748013000157

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