Weight zero Eisenstein cohomology of Shimura varieties via Berkovich spaces
type: Item
instance of: scholarly article
title: Weight zero Eisenstein cohomology of Shimura varieties via Berkovich spaces
zbMATH Open document ID: 1348.11047
author: Michael Harris
published in: Pacific Journal of Mathematics
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1208.1747
review text: The main aim of the article under review is to propose a geometric framework for the construction of weight zero Eisenstein classes in the cohomology of Shimura varieties, via Berkovich spaces. The idea begins with the abstract simplicial complex \(\Sigma\) defined by the configuration of boundary divisors of a toroidal compactification \(S'\) of a Shimura variety \(S\). In good situations, the associated Berkovich spaces \(|S|\) and \(|S'|\) (relative to a place \(v\) of the reflex field) will be contractible, and \(\Sigma\) will be homotopy equivalent to the boundary \(|S|'\smallsetminus |S|\). Using the long exact sequence on cohomology and a comparison isomorphism of Berkovich, one thus obtains an identification of the cohomology of \(\Sigma\) with the weight zero cohomology of \(S\) in degree one higher. In this article, the author carries through this idea in the simplest situation.
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14G35
Mathematics Subject Classification ID: 14G22
zbMATH DE Number: 6335994
zbMATH Keywords: Shimura varieties
zbMATH Keywords: Eisenstein cohomology
zbMATH Keywords: Berkovich spaces
reviewed by: Brian Smithling
MaRDI profile type: Publication
OpenAlex ID: W3102906112
arXiv ID: 1208.1747
DOI: 10.2140/PJM.2014.268.275
description: scientific article; zbMATH DE number 6335994