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Nearby Cycles for Local Models of Some Shimura Varieties

Published online by Cambridge University Press:  04 December 2007

T. Haines  and
B. C. Ngô
T. Haines
Affiliation:
Mathematics Department, University of Maryland, College Park, MD 20742, U.S.A. e-mail: tjh@math.umd.edu
B. C. Ngô
Affiliation:
Département de mathématiques, CNRS, Université de Paris Nord, 93430 Villetaneuse, France. e-mail: ngo@math.univ-paris13.fr
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Abstract

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Kottwitz conjectured a formula for the (semi-simple) trace of Frobenius on the nearby cycles for the local model of a Shimura variety with Iwahori-type level structure. In this paper, we prove his conjecture in the linear and symplectic cases by adapting an argument of Gaitsgory, who proved an analogous theorem in the equal characteristic case.

Keywords

nearby cycleslocal modelsShimura varietiesHasse–Weil zeta functionsHecke–Iwahori algebraBernstein center
Type
Research Article
Information
Compositio Mathematica , Volume 133 , Issue 2 , September 2002 , pp. 117 - 150
Copyright
© 2002 Kluwer Academic Publishers