On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz)

Sophie Morel

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arXiv · 0802.4451

On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz)

Sophie Morel

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Abstract

The goal of this paper is to calculate the trace of the composition of a Hecke correspondence and a (high enough) power of the Frobenius at a good place on the intersection cohomology of the Satake-Baily-Borel compactification of certain Shimura varieties, to stabilize the result for Shimura varieties associated to unitary groups over $\mathbb{Q}$ and to give applications of this calculations using base change from these unitary groups to $GL_n$. ----- Le but de ce texte est de calculer la trace d'une correspondance de Hecke composee avec une puissance (assez grande) du Frobenius en une bonne place sur la cohomologie d'intersection de la compactification de Satake-Baily-Borel de certaines varietes de Shimura, de stabiliser le resultat obtenu pour les varietes de Shimura associees aux groupes unitaires sur $\mathbb{Q}$, et de donner des applications de ces calculs en utilisant le changement de base de ces groupes unitaires a $GL_n$.

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Sophie Morel. 2008-02-29. On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz). https://arxiv.org/abs/0802.4451

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