Cohomology of quaternionic Shimura varieties at parahoric levels
type: Item
instance of: scholarly article
title: Cohomology of quaternionic Shimura varieties at parahoric levels
zbMATH Open document ID: 0996.11045
author: Harry Reimann
published in: Manuscripta Mathematica
publication date: 2002-06-17T00:00:00Z
review text: Let \(Sh_D\) be the Shimura variety associated to the multiplicative group \(D^\times\) of a quaternion division algebra \(D\) over a totally real number field \(F\). In this paper the author proves an identity between some semisimple \(L\)-functions associated to the cohomology of \(Sh_D\) and semisimple automorphic \(L\)-functions. By assuming a certain purity condition he also obtains a similar result for the usual \(L\)-functions. The main theorem in this paper extends the results in a previous paper by the author [Math. Ann. 317, 41-55 (2000; Zbl 1009.11045)] to a more general case.
reviewed by: Min Ho Lee
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 11G40
Mathematics Subject Classification ID: 14G35
zbMATH DE Number: 1756834
zbMATH Keywords: Shimura varieties
zbMATH Keywords: \(L\)-functions
zbMATH Keywords: automorphic forms
MaRDI profile type: Publication
full work available at URL: s002290200245
OpenAlex ID: W2018966291
DOI: 10.1007/S002290200245
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description: scientific article; zbMATH DE number 1756834