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Néron models and tame ramification. (English) Zbl 0759.14033
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.

MSC:
14K05 Algebraic theory of abelian varieties
14K15 Arithmetic ground fields for abelian varieties
13F30 Valuation rings
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References:
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