Speaker : Noah Riggenbach (Northwestern University)

Title : NTC of Perfectoid Rings

Abstract: In this talk I will discuss my recent computation of the NTC groups of perfectoid rings which have a system of pth power roots of unity and thus the KK-groups of the p-completed affine line R〈x〉R〈x〉 over these rings relative to the ideal (x)(x). This includes all perfect fields of positive characteristic, for which these groups vanish in non-negative degrees. This class of rings also contains many mixed characteristic rings, and perhaps surprisingly while the even nonnegative groups will still vanish, the odd groups will not.