Artin–Verdier duality

In mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by Michael Artin and Jean-Louis Verdier (1964), that generalizes Tate duality.

It shows that, as far as etale (or flat) cohomology is concerned, the ring of integers in a number field behaves like a 3-dimensional mathematical object.