Local-global principles for 1-motives
David Harari, Tamas Szamuely
Abstract
Building upon our arithmetic duality theorems for 1-motives, we prove that the Manin obstruction related to a finite subquotient (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.
Create a lesson
Related papers
An Infinite Family of Apéry-like Recurrences for Euler's Constant
Rotem Kalisch, Tali Monderer, Elyasheev Leibtag et al.
On the saturability of p-adic Lie groups
Casey Perdue
On Divisor Function Polynomials and Dirichlet Series
Martin N. Huxley, Matthew C. Lettington, Karl Michael Schmidt
On a conjecture on Romanoff type representations
Xiao-Hui Yan
Regularization of a Divergent Arithmetic Product via the Asymptotic Monoid: The Case of (-1)ω(n)
A. Alvarez Cruz, E. A. Alvarez Gutierrez
Appell Sequences in Analytic Number Theory: Shifted Expansions and Dirichlet L-Functions
Abdelmejid Bayad