On Local Models with Special Parahoric Level Structure

Details On Local Models with Special Parahoric Level Structure On Local Models with Special Parahoric Level Structure

2008-04-11

arxiv.org/abs/0804.1886v1

Michigan Math. J. Volume 58, Issue 3 (2009), 683-710

Mathematics

Algebraic Geometry

30 pages, 1 figure

Scientific paper

10.1307/mmj/1260475695

We consider the local model of a Shimura variety of PEL type, with the unitary similitudes corresponding to a ramified quadratic extension of $\mathbb{Q}_p$ as defining group. We examine the cases where the level structure at $p$ is given by a parahoric that is the stabilizer of a selfdual periodic lattice chain and that is special in the sense of Bruhat--Tits theory. We prove that in these cases the special fiber of the local model is irreducible and generically reduced; consequently, the special fiber is reduced and is normal, Frobenius split, and with only rational singularities. In addition, we show that in these cases the local model contains an open subset that is isomorphic to affine space.

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