Duality for complexes of tori over a global field of positive characteristic

TL;DR

This paper extends arithmetic duality theorems, including a Poitou-Tate sequence, to complexes of tori over global fields of positive characteristic, using duality for finite flat group schemes.

Contribution

It proves duality theorems for complexes of tori over positive characteristic global fields, analogous to those known over number fields, incorporating a Poitou-Tate sequence.

Findings

Establishes a Poitou-Tate exact sequence for Galois hypercohomology.

Adapts Artin-Mazur-Milne duality to complexes of tori.

Provides foundational results for local-global principles in positive characteristic.

Abstract

If K is a number field, arithmetic duality theorems for tori and complexes of tori over K are crucial to understand local-global principles for linear algebraic groups over K. When K is a global field of positive characteristic, we prove similar arithmetic duality theorems, including a Poitou-Tate exact sequence for Galois hypercohomology of complexes of tori. One of the main ingredients is Artin-Mazur-Milne duality theorem for fppf cohomology of finite flat commutative group schemes.