  We establish a formula for computing the unramified Brauer group of tame
conic bundle threefolds in characteristic 2. The formula depends on the
arrangement and residue double covers of the discriminant components, the
latter being governed by Artin-Schreier theory (instead of Kummer theory in
characteristic not 2). We use this to give new examples of threefold conic
bundles defined over the integers that are not stably rational over the complex
numbers.
