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

TLDR: In this paper, it was shown that the original local models are typically not flat and that the new local models can be shown to be topologically flat when is odd and when is even.

Abstract: Local models are schemes, defined in terms of linear-algebraic moduli problems, which are used to model the etale-local structure of integral models of certain -adic PEL Shimura varieties defined by Rapoport and Zink. In the case of a unitary similitude group whose localization at is ramified, quasi-split , 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 is odd. In the present paper, we prove topological flatness when is even. Along the way, we characterize the -admissible set for certain cocharacters in types and , and we show that for these cocharacters admissibility can be characterized in a vertexwise way, confirming a conjecture of Pappas and Rapoport.