linear case a result of V. Kathotia([@kathotia1998]).

Sections \[Cayleytree\] to \[proof\] are devoted to the proof of the Theorem \[th:main\]. In Section \[Cayleytree\] we introduce special graphs, the Cayley trees, which allow us to write down a perturbative version of the SGA equation. In Section \[sec:Konttrees\] we describe the Kontsevich trees. We use them to produce an explicit solution for the deformation problem. Section \[proof\] completes the proof of Theorem \[th:main\].

In the last section we come to the comparison with deformation quantization. We see that the Kontsevich star-product can be put into the form $$f*g(x) = \exp\Big(\frac{1}{h}\sum_{i=0}^{\infty}h^i D_i(h\partial_y,h\partial_z,x)\Big)f(y)g(z)_{\Big|y=z=x}$$ where $$S_h(p_1,p_2,x) =x(p_1+p_2)+\frac{1}{h} D_0(h p_1,h p_2,x).$$ This allows us to interpret the generating function as a semi-classical version of the Kontsevich star-product formula. At last, considering associativity of star product of exponential functions, we are able to provide an elegant but non-rigourous proof of the existence part of Theorem \[th:main\].

Planned developements
---------------------

One of the next objective is to carry the construction of the formal symplectic groupoid to a general Poisson manifold. Such a globalisation has already been made by Karabegov [@karabegov2003] in the symplectic case.

A second possible developement is to try to derive the existence of the deformation 