Local-global principles for 1-motives
| dc.creator | Harari, David | |
| dc.creator | Szamuely, Tamas | |
| dc.date | 2007-03-28 | |
| dc.date | 2007-09-28 | |
| dc.date.accessioned | 2026-07-07T08:32:42Z | |
| dc.date.available | 2026-07-07T08:32:42Z | |
| dc.description | Building upon our arithmetic duality theorems for 1-motives, we prove that the Manin obstruction related to a finite subquotient $\Be (X)$ 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-Shaferevich 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. | |
| dc.description | 23 pages, minor modifications | |
| dc.identifier | https://arxiv.org/abs/math/0703845 | |
| dc.identifier | http://arxiv.org/abs/math/0703845 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/138875 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14G25 | |
| dc.title | Local-global principles for 1-motives | |
| dc.type | text |