Néron models
type: Item
instance of: scholarly article
title: Néron models
zbMATH Open document ID: 1396.14038
published in: European Journal of Mathematics
publication date: 2017-11-10T00:00:00Z
review text: The paper under review is a review (survey) article on Néron models which is a written version of a series of lectures delivered at the Sino-French Conference in Algebraic and Arithmetic Geometry in Bordeaux, France, May 23--27, 2016. The author of the paper under review started by mentioning some historical background of Néron models in the Introduction. ``Néron models were introduced by André Néron (1922--1985) in his seminar at the IHÉS in 1961''. ``Néron's own full account of his theory is found in [\textit{A. Neron}, Publ. Math., Inst. Hautes Étud. Sci. 21, 128 (1964; Zbl 0132.41403)]. Unfortunately, this article is not completely written in the modern language of algebraic geometry.'' Then he mentions some major references in the language of schemes, including ``the 1990 book [Néron models. Berlin etc.: Springer-Verlag (1990; Zbl 0705.14001)] by \textit{S. Bosch} et al.,'' which ``remains the most detailed source of information.'' After the Introduction, the remaining sections consist of ``Models, (Strong) Néron models, (Weak) Néron models, The Néron models of an abelian variety, The Néron model of a Jacobian'', and ``The group of components'', where in the last section, a conjecture was posed regarding the size of a quotient of the group of components of some abelian variety. This short survey consists of 24 pages in the main text and 4 pages listing 111 references including the past and more recent results. The survey also provides many examples contributing to better understanding for readers new in the area.
reviewed by: Cherng-tiao Perng
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 14L15
zbMATH DE Number: 6805515
zbMATH Keywords: Néron model
zbMATH Keywords: weak Néron model
zbMATH Keywords: abelian variety
zbMATH Keywords: group scheme
zbMATH Keywords: elliptic curve
zbMATH Keywords: semi-stable reduction
zbMATH Keywords: Jacobian
zbMATH Keywords: group of components
author: Dino Lorenzini
MaRDI profile type: Publication
full work available at URL: s40879-017-0134-8
OpenAlex ID: W3188408157
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Néron models (DOI)
DOI: 10.1007/S40879-017-0134-8

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