perfectoid signature and local étale fundamental group abstract: in this talk i'll talk about a (perfectoid) mixed characteristic version of f-signature and hilbert-kunz multiplicity by utilizing the perfectoidization functor of bhatt-scholze and faltings' normalized length. these definitions coincide with the classical theory in equal characteristic. moreover, perfectoid signature detects bcm regularity and transforms similarly to f-signature or normalized volume under quasi-étale maps. as a consequence, we can prove that bcm-regular
rings have finite local étale fundamental group and torsion part of their divisor class groups. this is joint work with seungsu lee, linquan ma, karl schwede and kevin tucker.

[pre-talk at 1:20pm]