# 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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