  The paper deals with the homogenization of a linear Boltzmann equation by the
means of the sigma-convergence method. Under a general deterministic assumption
on the coefficients of the equation, we prove that the density of the particles
converges to a solution of a drift-diffusion equation. To achieve our goal, we
use the Krein-Rutman theorem for locally convex spaces together with the
Fredholm alternative to solve the so-called corrector problem.
