Abstract
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
Citation
David Harari. Tamás Szamuely. "Local-global principles for -motives." Duke Math. J. 143 (3) 531 - 557, 15 June 2008. https://doi.org/10.1215/00127094-2008-028
Information