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

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Abstract

In this article, we present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties over -adic fields in terms of the Néron-Severi group and provide a proof under additional assumptions on an integral model of . 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 for the Albanese cokernel; the abelian group on the 'local side' turns out to be a finite group.

Original languageEnglish
Pages (from-to)1915-1934
Number of pages20
JournalCompositio Mathematica
Volume152
Issue number9
DOIs
Publication statusPublished - 2016 Sep 1
Externally publishedYes

Keywords

  • Albanese map
  • Brauer groups

ASJC Scopus subject areas

  • Algebra and Number Theory

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