Summary: In this paper we aim at completing the study of \(\sigma \)-complete Riesz MV-algebras that started in Di Nola et al. (2018, J. Logic Comput., 28, 1275-1292). To do so, we discuss polynomials, algebraic geometry and dualities in the infinitary variety of such algebras. In particular, we characterize the free objects as algebras of Baire-measurable functions and we generalize two dualities, namely the Marra-Spada duality and the Gelfand duality, obtaining a duality with basically disconnected compact Hausdorff spaces and an equivalence with Rickart \(C^*\)-algebras.