Duke Mathematical Journal

Local-global principles for 1-motives

David Harari and Tamás Szamuely

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Building upon our arithmetic duality theorems for 1-motives, we prove that the Manin obstruction related to a finite subquotient Б(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

Article information

Duke Math. J., Volume 143, Number 3 (2008), 531-557.

First available in Project Euclid: 3 June 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G25: Global ground fields
Secondary: 14G05: Rational points


Harari, David; Szamuely, Tamás. Local-global principles for $1$ -motives. Duke Math. J. 143 (2008), no. 3, 531--557. doi:10.1215/00127094-2008-028. https://projecteuclid.org/euclid.dmj/1212500466

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