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- Title
A higher-dimensional generalization of Lichtenbaum duality in terms of the Albanese map.
- Authors
Kai, Wataru
- Abstract
In this article, 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 for the Albanese cokernel; the abelian group on the ‘local side’ turns out to be a finite group.
- Subjects
INTEGRAL geometry; COHOMOLOGY theory; NON-degenerate perturbation theory; BRAUER groups; AZUMAYA algebras
- Publication
Compositio Mathematica, 2016, Vol 152, Issue 9, p1915
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X16007600