# looking for a proof or a reference of classical result

Let $$X$$ be a complex manifold of dimension $$n$$, $$\Omega_{X}$$ the sheaf of top degree forms, $$\mathcal{D}_{X}$$ the sheaf of holomorphic differential operators of infinite order and $$q$$ the natural projection of $$X\times X$$ to $$X$$. It seems to be known that $$\mathcal{D}_{X}\simeq H^{n}_{\Delta_{X}}(q^{-1}\Omega_{X}\otimes_{q^{-1}\mathcal{O}_{X}}\mathcal{O}_{X\times X})$$.

Is there any good reference of this ?

• Just a suggestion: if you tell where you found this result, it might be easier to find the reference you need – Yuriy S Oct 13 '18 at 23:40
• @YuriyS Kashiwara-Shapira, "Sheaves on Manifold", definition 11.4.2, however this is stated in a more general context of micro-differential operators – epsilones Oct 13 '18 at 23:57