## 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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