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15 January 2001 Test functions for Shimura varieties: the Drinfeld case
Thomas J. Haines
Duke Math. J. 106(1): 19-40 (15 January 2001). DOI: 10.1215/S0012-7094-01-10612-1

Abstract

A recent conjecture of Kottwitz predicts that certain central elements in Iwahori-Hecke algebras play an important role in the bad reduction of Shimura varieties with Iwahori level structure. Namely, the function trace of Frobenius on nearby cycles is conjecturally expressible in terms of the so-called Bernstein function zμ corresponding to the cocharacter μ coming from the Shimura data. In this paper we prove an explicit formula for zμ in terms of the standard basis for the Iwahori-Hecke algebra, for any minuscule cocharacter μ of any p-adic group G. We then use this formula to prove Kottwitz's conjecture for a particular Shimura variety, attached to G=GU(1,d−1) and μ=(1,0d−1), known as the "Drinfeld case."

Citation

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Thomas J. Haines. "Test functions for Shimura varieties: the Drinfeld case." Duke Math. J. 106 (1) 19 - 40, 15 January 2001. https://doi.org/10.1215/S0012-7094-01-10612-1

Information

Published: 15 January 2001
First available in Project Euclid: 13 August 2004

zbMATH: 1014.20002
MathSciNet: MR1810365
Digital Object Identifier: 10.1215/S0012-7094-01-10612-1

Subjects:
Primary: 11G18
Secondary: 20C08

Rights: Copyright © 2001 Duke University Press

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Vol.106 • No. 1 • 15 January 2001
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