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The Brauer–Manin obstruction for subvarieties of abelian varieties over function fields
, 2008
"... We prove that for a large class of subvarieties of abelian varieties over global function fields, the BrauerManin condition on adelic points cuts out exactly the rational points. This result is obtained from more general results concerning the intersection of the adelic points of a subvariety with ..."
Abstract

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We prove that for a large class of subvarieties of abelian varieties over global function fields, the BrauerManin condition on adelic points cuts out exactly the rational points. This result is obtained from more general results concerning the intersection of the adelic points of a subvariety with the adelic closure of the group of rational points of the abelian variety.