The Langlands-Kottwitz approach for some simple Shimura varieties
type: Item
instance of: scholarly article
title: The Langlands-Kottwitz approach for some simple Shimura varieties
zbMATH Open document ID: 1309.14020
author: Peter Scholze
published in: Inventiones Mathematicae
publication date: 2013-06-18T00:00:00Z
full work available at URL: https://arxiv.org/abs/1003.2451
review text: In a previous paper [Int. Math. Res. Not. 2011, No. 15, 3368--3425 (2011; Zbl 1309.14019)] the author extended techniques of Langlands and Kottwitz to determine the local factors of the Hasse-Weil zeta functions of modular curves at primes of bad reduction. Those methods are extended in this paper to obtain the semisimple Hasse-Weil zeta-function of Shimura varieties associated with unitary groups of real rank \(1\). A key part of the proof is the calculation of the semisimple Lefschetz number in terms of orbital integrals, and thus establishing a special case of a conjecture of Haines and Kottwitz.
reviewed by: Salman Abdulali
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 6176661
zbMATH Keywords: Shimura variety
zbMATH Keywords: Hasse-Weil zeta function
zbMATH Keywords: unitary group
zbMATH Keywords: orbital integral
MaRDI profile type: Publication
OpenAlex ID: W2072883943
arXiv ID: 1003.2451
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DOI: 10.1007/S00222-012-0419-Y
description: scientific article