# Perfectoid multiplier ideals

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Linquan Ma, University of Utah
Fine Hall 322

Inspired by the recent solution of the direct summand conjecture of Yves Andre, we introduce perfectoid multiplier/test ideals in mixed characteristic. As an application, we obtain a uniform bound on the growth of symbolic powers in regular local rings of mixed characteristic analogous to results of Ein-Lazarsfeld-Smith and Hochster-Huneke in equal characteristic. This is joint work with Karl Schwede.