15 February 2009 Counting points on Igusa varieties
Sug Woo Shin
Author Affiliations +
Duke Math. J. 146(3): 509-568 (15 February 2009). DOI: 10.1215/00127094-2009-004

Abstract

Igusa varieties are smooth varieties over F̲p which are higher-dimensional analogues of Igusa curves. They were introduced by Harris and Taylor [HT] to study the bad reduction of some PEL Shimura varieties and were generalized by Mantovan [M1], [M2]. The present article gives a group-theoretic formula for the traces of certain operators on the cohomology of Igusa varieties, suitable for applications via comparison with the Arthur-Selberg trace formula. Our formula generalizes the results of [HT, Chap. V, Prop. 4.8] to the case of any PEL Shimura varieties of types (A) and (C) and puts it in a more natural framework, in the spirit of [K7]

Citation

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Sug Woo Shin. "Counting points on Igusa varieties." Duke Math. J. 146 (3) 509 - 568, 15 February 2009. https://doi.org/10.1215/00127094-2009-004

Information

Published: 15 February 2009
First available in Project Euclid: 14 January 2009

zbMATH: 1218.11061
MathSciNet: MR2484281
Digital Object Identifier: 10.1215/00127094-2009-004

Subjects:
Primary: 11G15
Secondary: 11F72 , 11R39

Rights: Copyright © 2009 Duke University Press

Vol.146 • No. 3 • 15 February 2009
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