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arXiv · 1512.02026

A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map

Wataru Kai
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Abstract

We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms of the Néron-Severi group and provide a proof under additional assumptions on an integral model of $X$. The proof depends on a non-degeneracy result of Brauer-Manin pairing due to Saito-Sato and on Gabber-de Jong's comparison result of cohomological- and Azumaya-Brauer groups. We will also mention the local-global problem of the Albanese-cokernel; the abelian group on the "local side" turns out to be a finite group.

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Wataru Kai. 2016-04-27. A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map. https://doi.org/10.1112/s0010437x16007600

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