A toroidal resolution for the bad reduction of some Shimura varieties
Abstract
Borrowing a reduction principle to a recent preprint of G. Faltings (toroidal resolution of some matrix singularities, 1999), we use Lafforgue's compactification of PGLrN+1/PGLr to construct a canonical log-smooth toroidal resolution for the bad reduction in a prime p of Shimura varieties of unitary and symplectic type with parahoric level structures at p. Using this result, non-canonical semi-stable resolutions over Zp[p1/] can be derived.
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