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Reference request: Formal Existence for stacks

Is there a formal existence Theorem for coherent sheaves on locally Noetherian Artin Stacks, in the spirit of Grothendieck's Formal GAGA? Is it available for more general stacks?
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Frobenius stratification of imperfect fields

Suppose $k$ is a (non-perfect) field of characteristic $p$, and $Fr$, its Frobenius map. I’d appreciate comments and references on the structure of the fitration/stratification of $k$ given by the ...
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