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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 ?

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

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