# Perfectoid approach to resolution of singularities in char $p$

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?

• 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). – Hailong Dao Mar 26 at 19:43
• @HailongDao, I too am waiting for him, like Gogo for Godot. – Arna Mar 26 at 20:02
• 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. – Faris Mar 27 at 6:19