Théorèmes de dualité pour les complexes de tores

Details Théorèmes de dualité pour les complexes de tores Théorèmes de dualité pour les complexes de tores

2009-06-18

arxiv.org/abs/0906.3453v1

Mathematics

Number Theory

44 pages

Scientific paper

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. In particular, we obtain a Poitou-Tate exact sequence for k-groups of multiplicative type. The general results proven here lie at the root of recent results 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.

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