Abstract: We use the action of the Bockstein homomorphism on the mod 2 cohomology ring of a finite-type CW-complex in order to define its resonance varieties in characteristic 2. Much of the theory is done in the more general framework of the Maurer-Cartan sets and the resonance varieties attached to a finite-type commutative differential graded algebra in arbitrary characteristic. We illustrate these concepts with examples mainly drawn from closed manifolds, where Poincar\’e duality over Z_2 has strong implications on the nature of the resonance varieties.