Poitou-Tate duality over extensions of global fields

TL;DR

This paper develops a derived category framework for Poitou-Tate duality, extending classical Galois cohomology dualities to a more general setting involving pro-p rings and compact modules.

Contribution

It introduces a derived category formulation of Poitou-Tate duality for Galois cohomology over pro-p rings, broadening the scope of classical duality results.

Findings

Established a derived category version of Poitou-Tate duality.

Extended duality to Galois cohomology of compact modules over pro-p rings.

Provided new tools for studying Galois cohomology in a derived setting.

Abstract

In this paper, we formulate and prove a derived category version of Poitou-Tate duality on Galois cohomology of compact modules (with a continuous Galois action) over a pro-p ring, where p is a prime.