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Some folklore about crystaline rings of differential operators

Proposition 1* does follow from that $\mathcal D_c$ sheafifies. For if $k(X) \cong k(Y)$, then $X$ and $Y$ are birational, so there are affine open subsets $U \subseteq X$, $V \subseteq Y$ such that $...
Joshua Mundinger's user avatar
3 votes

Relation between enveloping algebras and algebras of differential operators

As you guessed, the kernel will be infinite dimensional (at least for $\dim X \geq 1$). To see this, you can take the order filtration on $\mathcal D(X)$ and the PBW filtration on $U(\mathcal V_X)$. ...
Phil Tosteson's user avatar

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