Mathematical Research Letters

Volume 28 (2021)

Number 5

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

Pages: 1551 – 1593



Yisheng Tian (Department of Mathematics, Université Paris-Saclay, Orsay, France)


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.

Received 14 November 2019

Accepted 25 April 2020

Published 16 August 2022