English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a complex of tori of length 2 defined over a number field k. Weestablish here some local and global duality theorems for the (\'etale orGalois) hypercohomology of such a complex. We prove the existence of aPoitou-Tate exact sequence for such a complex, which generalizes thePoitou-Tate exact sequences for finite Galois modules and tori. In particular,we obtain a Poitou-Tate exact sequence for k-groups of multiplicative type. Thegeneral results proven here lie at the root of recent results about the defectof strong approximation in connected linear algebraic groups and about somearithmetic duality theorems for the (non-abelian) Galois cohomology of suchgroups.

Th\'eor\`emes de dualit\'e pour les complexes de tores