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Since perfectoid techniques have built a bridge between char $0$ and char $p$ worlds, it is conceivable that they can be applied to resolution of singularities in char $p$ using their successful resolution in char $0$, or offer an alternative view of alterations. Has this been attempted, and if not, why is it not a plausible line of approach?

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    $\begingroup$ While we wait for Peter to answer, my impression is that the perfectoid approach allows us to mimic techniques in char $p>0$ that were used to make up for the lack of resolution of singularity such as Frobenius and existence of big Cohen-Macaulay algebras (which allow us to prove vanishing results up to finite covers). $\endgroup$ – Hailong Dao Mar 26 at 19:43
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    $\begingroup$ @HailongDao, I too am waiting for him, like Gogo for Godot. $\endgroup$ – Arna Mar 26 at 20:02
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    $\begingroup$ I think a lot of interest is in resolutions over fields algebraic over their prime subfields and I doubt perfectoids would help in that setting. $\endgroup$ – Faris Mar 27 at 6:19

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