Néron models
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.
scientific article; zbMATH DE number 6805515
scientific article