Poitou--Tate sequence for complex of tori over $p$-adic function fields

TL;DR

This paper extends local and global duality theorems to complexes of tori over p-adic function fields, establishing a 12-term Poitou--Tate sequence linking global and local Galois cohomology.

Contribution

It completes the duality framework for complexes of tori over p-adic function fields and derives a comprehensive Poitou--Tate exact sequence.

Findings

Established a 12-term Poitou--Tate sequence.

Unified local and global duality theorems for complexes of tori.

Connected global Galois cohomology with local cohomology via exact sequence.

Abstract

We complete the picture of local and global arithmetic duality theorems for short complexes of finite Galois modules and tori over $p$-adic function fields. In view of the duality theorems, we deduce a $12$-term Poitou--Tate exact sequence which relates global Galois cohomology groups to restricted topological products of local Galois cohomology groups.