Topological flatness of local models for ramified unitary groups. I. The odd dimensional case |
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Authors: | Brian D Smithling |
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Institution: | University of Toronto, Department of Mathematics, 40 St. George St., Toronto, ON M5S 2E4, Canada |
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Abstract: | Local models are certain 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. When the group defining the Shimura variety ramifies at p, the local models (and hence the Shimura models) as originally defined can fail to be flat, and it becomes desirable to modify their definition so as to obtain a flat scheme. In the case of unitary similitude groups whose localizations at Qp are ramified, quasi-split GUn, Pappas and Rapoport have added new conditions, the so-called wedge and spin conditions, to the moduli problem defining the original local models and conjectured that their new local models are flat. We prove a preliminary form of their conjecture, namely that their new models are topologically flat, in the case n is odd. |
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Keywords: | MSC: primary 14G35 secondary 05E15 11G18 17B22 |
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