Poitou-Tate suites for two complex tori terms

We consider a complex of tori of length 2 defined over a number field k. We establish here some local and global duality theorems for the (etale or Galois) hypercohomology of such a complex. We prove the existence of a Poitou-Tate exact sequence for such a complex, which generalizes the Poitou-Tate exact sequences for finite Galois modules and tori. The general results proven here lie at the root of recent results by the author about the defect of strong approximation in connected linear algebraic groups and about some arithmetic duality theorems for the (non-abelian) Galois cohomology of such groups.