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Frobenius Descent
A result by Cartier (often called Cartier descent or Frobenius descent) then states that the category of quasi-coherent $\mathcal{O}_{X^{(p)}}$-modules is equivalent to the category of quasi-coherent $ … In other words, does the connection $\nabla$ give rise to a descent datum for $E$ with respect to $F$? …