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Duality theorems for Néron models. (English) Zbl 0623.14023
Let R be a complete discrete valuation ring with finite residue field and let K be its fraction field. For every abelian variety \(A_ K\) over K let A be its Néron model over Spec(R). The author proves a duality theorem for the Néron model A which extends the Tate’s duality for the abelian variety \(A_ K\). Moreover, under suitable hypothesis, he deduces a flat duality theorem for A[n], the kernel of multiplication by n. - The proof uses the properties of Néron models and the biextensions.
Reviewer: L.Picco Botta

MSC:
14K05 Algebraic theory of abelian varieties
14E30 Minimal model program (Mori theory, extremal rays)
13F30 Valuation rings
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