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I am learning about $D$-module theory and came across a theorem that says that coherent equivariant $D$-modules whose support has finitely many orbits are automatically regular holonomic. Are there examples where the converse statement is false?

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  • $\begingroup$ D-modules make sense on spaces that have no group action, so this question doesn't make much sense. Take, for example, the $\mathcal D$-module $\mathcal O_{\mathbb A^1}$, and use the trivial group action on ${\mathbb A^1}$. $\endgroup$ – Allen Knutson Apr 27 '16 at 17:17

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