Edixhoven, Bas Néron models and tame ramification. (English) Zbl 0759.14033 Compos. Math. 81, No. 3, 291-306 (1992). The author treats the behaviour of Néron models of abelian varieties with respect to tamely ramified extensions of discrete valuation rings. More precisely, let \(D'\succ D\) be a tamely ramified Galois extension of discrete valuation rings with Galois group \(G\) and with fields of fractions \(K'\succ K\). Let \(A\) be an abelian variety over \(K\). Under these notations, the author shows that the Néron model \({\mathcal A}\) of \(A\) over \(D\) is given by the \(G\)-invariant locus of the Weil restriction \(\Pi_{D'/D}({\mathcal A}'/D')\) of the Néron model \({\mathcal A}'\) of \(A'=A_{K'}\) over \(D'\). Using this result, he discusses the exactness of Néron models relevant to the absolute ramification index. Reviewer: T.Sekiguchi (Tokyo) Cited in 8 ReviewsCited in 37 Documents MSC: 14K05 Algebraic theory of abelian varieties 14K15 Arithmetic ground fields for abelian varieties 13F30 Valuation rings Keywords:Néron models of abelian varieties; tamely ramified extensions of discrete valuation rings; Weil restriction PDF BibTeX XML Cite \textit{B. Edixhoven}, Compos. Math. 81, No. 3, 291--306 (1992; Zbl 0759.14033) Full Text: Numdam EuDML OpenURL References: [1] S. Bosch , W. Lütkebohmert and M. Raynaud , Néron models , Springer Verlag, Ergebnisse 3, 21 (1990). · Zbl 0705.14001 [2] A. Grothendieck , Fondements de la géométrie algébrique , Sém. Bourbaki, exposés 149, 182, 190, 195, 212, 221, 232, 236, (1956-1962). · Zbl 0239.14001 [3] A. Grothendieck , Séminaire de géométrie algébrique , Springer Lecture Notes in Mathematics 151, 152, 153, 224, 225, 269, 270, 288, 305, 340, 589. [4] A. Grothendieck , Éléments de géométrie algébrique , Publications Mathématiques de l’I.H.E.S. 4, 8, 11, 17, 20, 24, 28, 32 (1960-1967). | [5] M. Raynaud , Spécialisation du foncteur de Picard , Publications Mathématiques de l’I.H.E.S. 38 (1970). · Zbl 0207.51602 [6] M. Raynaud , Schémas en groupes de type (p,..., p) . Bull. Soc. Math. France 102, 241-280 (1974). · Zbl 0325.14020 [7] J. Tate , Algorithm for determining the type of a singular fibre in an elliptic pencil . In Modular Functions of One Variable IV , 33-52. Springer Lecture Notes in Mathematics 476 (1975). · Zbl 1214.14020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.