Local-global principles for $1$-motives
David Harari and Tamás Szamuely
Source: Duke Math. J. Volume 143, Number 3
(2008), 531-557.
Abstract
Building upon our arithmetic duality theorems for $1$-motives, we prove that the Manin obstruction related to a finite subquotient ${\cyrille B} (X)$ of the Brauer group is the only obstruction to the Hasse principle for rational points on torsors under semiabelian varieties over a number field, assuming the finiteness of the Tate-Shafarevich group of the abelian quotient. This theorem answers a question by Skorobogatov in the semiabelian case and is a key ingredient of recent work on the elementary obstruction for homogeneous spaces over number fields. We also establish a Cassels-Tate-type dual exact sequence for $1$-motives and give an application to weak approximation
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1212500466
Digital Object Identifier: doi:10.1215/00127094-2008-028
Zentralblatt MATH identifier: 1155.14020
Mathematical Reviews number (MathSciNet): MR2423762
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