  We describe a globalization construction for the Rozansky-Witten model in the
BV-BFV formalism for a source manifold with and without boundary in the
classical and quantum case. After having introduced the necessary background,
we define an AKSZ sigma model, which, upon globalization through notions of
formal geometry extended appropriately to our case, is shown to reduce to the
Rozansky-Witten model. The relations with other relevant constructions in the
literature are discussed. Moreover, we split the model as a $BF$-like theory
and we construct a perturbative quantization of the model in the quantum BV-BFV
framework. In this context, we are able to prove the modified differential
Quantum Master Equation and the flatness of the quantum Grothendieck BFV
operator. Additionally, we provide a construction of the BFV boundary operator
in some cases.
