Arithmetic Duality Theorems for 1-Motives

We prove several duality theorems for the Galois and etale cohomology of 1-motives defined over local and global fields and establish a 12-term Poitou-Tate type exact sequence. The results give a common generalisation and sharpening of well-known theorems by Tate on abelian varieties as well as results by Tate/Nakayama and Kottwitz on algebraic tori.Comment: 44 pages, LaTeX, final version. Section 5 substantially rewritte

Local-global principles for 1-motives

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.Comment: 23 pages, minor modification

Weak approximation for tori over pp-adic function fields

This is the companion piece to "Local-global questions for tori over p-adic function fields" by the first and third authors. We study local-global questions for Galois cohomology over the function field of a curve defined over a p-adic field, the main focus here being weak approximation of rational points. We construct a 9-term Poitou--Tate type exact sequence for tori over a field as above (and also a 12-term sequence for finite modules). Like in the number field case, part of the sequence can then be used to analyze the defect of weak approximation for a torus. We also show that the defect of weak approximation is controlled by a certain subgroup of the third unramified cohomology group of the torus.Comment: final version, to appear in IMR

An analysis of humanitarian intervention in action

This submission examines the doctrine of humanitarian intervention by focusing on the Western involvement in the violent breakup of the Socialist Federal Republic of Yugoslavia during the 1990s and the wars that this ignited. It draws on several publications written over the past decade including "Securing Verdicts: The Misuse of Witness Evidence at The Hague", in Herman E.S. (ed), The Srebrenica Massacre: Evidence, Context, Politics (Szamuely 2011); Herman E.S., Peterson D. & Szamuely G., 2007, "Yugoslavia: Human Rights Watch in Service to the War Party" (Szamuely 2007); and Bombs for Peace: NATO’s Humanitarian War on Yugoslavia (Szamuely, 2014). Academic writers as well as policymakers deem NATO’s bombing of Bosnia in 1994 and 1995 and of Kosovo in 1999 to be exemplars of the successful use of force to secure humanitarian outcomes. This submission examines these claims in light of the standards that the advocates of humanitarian intervention have themselves put forward in order to measure the success or otherwise of any military action undertaken to stop mass atrocities and to save endangered civilians. My findings suggest that, even judged by those standards, NATO’s actions in Bosnia and Kosovo fell well short of success. Far more could have been achieved had diplomatic options been pursued with greater vigor than they actually were

Local-global principles for 1-motives

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