The kernel of the reciprocity map of simple normal crossing varieties over finite fields
type: Item
instance of: scholarly article
title: The kernel of the reciprocity map of simple normal crossing varieties over finite fields
zbMATH Open document ID: 1331.14031
DOI: 10.2977/PRIMS/91
author: Patrick Forré
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 2013-01-17T00:00:00Z
review text: Summary: For a smooth and proper variety \(Y\) over a finite field \(k\) the reciprocity map \(\rho^Y: \text{CH}_0(Y) \to \pi_1^{ab}(Y)\) is injective with dense image. For a proper simple normal crossing variety this is no longer true in general. In this paper we give a discription of the kernel and cokernel of the reciprocity map in terms of homology groups of a complex filled with descent data using an algebraic Seifert-van-Kampen theorem. Furthermore, we give a new criterion for the injectivity of the reciprocity map for proper simple normal crossing varieties over finite fields.
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 11G25
Mathematics Subject Classification ID: 11G45
zbMATH DE Number: 6126567
zbMATH Keywords: higher dimensional class field theory
zbMATH Keywords: reciprocity map
zbMATH Keywords: abelianized fundamental group
zbMATH Keywords: Seifert-van Kampen theorem
zbMATH Keywords: simple normal crossing varieties over finite fields
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.2977/prims/91
OpenAlex ID: W2012388514
description: scientific article; zbMATH DE number 6126567