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ag.algebraic geometry – Are equivariant wayward sheaves constructible with respect to the orbit stratification? Answer

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ag.algebraic geometry – Are equivariant wayward sheaves constructible with respect to the orbit stratification?

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Consider a spread $X$ over a bailiwick $okay$ (complicated numbers is exquisite) with the motion of a bunch strategy $G$, and a $G$-equivariant wayward sheaf $F$ over $X$. Is it undoubted that there exists a stratification $tau$ of $X$ which is $G$-equivariant and such that $F$ is $tau$-constructible? For instance, one might leer the orbit stratification.

I’m making an attempt to employ the characterisation of invariant wayward sheaves as these wayward sheaves such that $act^* Fsimeq pr_2^*F$ the place $act:Gtimes_k Xto X$ is the motion and $pr_2:Gtimes Xto X$ is the second projection. But I can not discover the answer.

Thank you in forward.

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