Duke Mathematical Journal
- Duke Math. J.
- Volume 143, Number 3 (2008), 531-557.
Local-global principles for -motives
Building upon our arithmetic duality theorems for -motives, we prove that the Manin obstruction related to a finite subquotient 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 -motives and give an application to weak approximation
Duke Math. J. Volume 143, Number 3 (2008), 531-557.
First available in Project Euclid: 3 June 2008
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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