Titlebook: Néron Models; Siegfried Bosch,Werner Lütkebohmert,Michel Raynaud Book 1990 Springer-Verlag Berlin Heidelberg 1990 Abelsche Variet?ten.Alge

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Construction of Birational Group Laws,In the previous chapter, we discussed the smoothening process and, as an application, proved the existence of weak Néron models. The next step towards the construction of Néron models requires the use of group arguments.

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Some Background Material from Algebraic Geometry, is familiar with Grothendieck’s definition of schemes and morphisms, we treat the concept of smooth and étale morphisms, of henselian rings, and of .-rational maps; moreover, we have included some facts on differential calculus and on flatness. Concerning the smoothness, we give a self-contained ex

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,Properties of Néron Models,For example, Néron models do not, in general, commute with (ramified) based change; also, in the group scheme case, the behavior with respect to exact sequences can be very capricious. The situation stabilizes somewhat if one considers Néron models with semi-abelian reduction.

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The Picard Functor,. The main purpose of this chapter is the presentation of various results on the representability of Pic.. We explain Grothendieck’s theorem on the representability of Pic. by a scheme and point out improvements due to Mumford [2] as well as those due to Altman and Kleiman [1]. In Section 8.3, we di

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Jacobians of Relative Curves,.. Then, in the last three sections, we work over a base . consisting of a discrete valuation ring . with field of fractions . and, applying these results, we investigate the relationship between Pic. and the Néron model of the Jacobian . of the generic fibre ..

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