Algebraic Geometry Seminar

Suppose D is a prime divisor in a normal scheme X. Inversion of adjunction for log terminal singularities says that the pair (X, D) is purely log terminal (PLT) if and only if (D, diff) is Kawamata log terminal (KLT), where diff, or the different, can be viewed as a correction term. Takagi proved a version of this result for F-regular singularities. In this talk, I will discuss joint work with Ma, Tucker, Waldron and Witaszek which generalizes these results to mixed characteristic schemes via perfectoid big Cohen-Macaulay (BCM) algebras. As an application, we obtain better understanding of mixed characteristic perfectoid BCM test ideals as well as an improved Briancon-Skoda formula in singular mixed characteristic rings.
Speaker(s): Karl Schwede (Utah)