Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Local models in the ramified case. I: The EL-case

Authors: G. Pappas and M. Rapoport
Journal: J. Algebraic Geom. 12 (2003), 107-145
Published electronically: July 18, 2002
MathSciNet review: 1948687
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Abstract | References | Additional Information

Abstract: Local models are schemes defined in linear algebra terms that describe the étale local structure of integral models for Shimura varieties and other moduli spaces. We point out that the flatness conjecture of Rapoport-Zink on local models fails in the presence of ramification and that in that case one has to modify their definition. We study modifications of the local models for $G=\text{\rm R}_{E/F}\text{\rm GL}(n)$, with $E/F$ a totally ramified extension, and for a maximal parahoric level subgroup. The special fibers of these models are subschemes of the affine Grassmannian. We give applications to the structure of Schubert varieties in the affine Grassmannian and to the calculation of sheaves of nearby cycles and describe a relation with geometric convolution. In the general EL case, we replace the conjecture of Rapoport-Zink with a conjecture about the modified local models.

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Additional Information

G. Pappas
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

M. Rapoport
Affiliation: Mathematisches Institut der Universität zu Köln, Weyertal 86-90, 50931 Köln, Germany

Received by editor(s): August 30, 2000
Received by editor(s) in revised form: November 27, 2001
Published electronically: July 18, 2002
Additional Notes: The first author was partially supported by NSF grant DMS99-70378 and by a Sloan Research Fellowship

American Mathematical Society