On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
type: Item
instance of: scholarly article
zbMATH Open document ID: 1251.14014
author: Jörg Wildeshaus
publication date: 2012-06-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/0906.4239
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 11G18
zbMATH DE Number: 6043645
zbMATH Keywords: Shimura variety
zbMATH Keywords: Hilbert-Blumenthal variety
zbMATH Keywords: motive
zbMATH Keywords: Chow motive
zbMATH Keywords: interior motive
zbMATH Keywords: Kuga-Satake family
zbMATH Keywords: weight structure
zbMATH Keywords: purity
MaRDI profile type: Publication
OpenAlex ID: W2140172269
arXiv ID: 0906.4239
DOI: 10.1093/IMRN/RNR109
published in: IMRN. International Mathematics Research Notices
title: On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
review text: The paper under review constructs and analyses a Hecke equivariant Chow motive for Hilbert-Blumenthal varieties associated to a fixed totally real number field \(L\). This so-called \textit{interior motive} has interior (or intersection) cohomology of Hilbert-Blumenthal varieties as its realisations. The construction is in perfect analogy with the case of classical modular forms (i.e.~Hilbert-Blumenthal varieties for \(L=\mathbb{Q}\)). In comparison to the approaches of Deligne and Scholl in the classical case, the author develops alternative strategies based on Bondarko's formalism of weight structures.
reviewed by: Matthias Schütt
description: scientific article; zbMATH DE number 6043645