Uniform approximation of Abhyankar valuation ideals in mixed characteristic - Rankeya Datta скачать в хорошем качестве

Uniform approximation of Abhyankar valuation ideals in mixed characteristic - Rankeya Datta

Title: Uniform approximation of Abhyankar valuation ideals in mixed characteristic Abstract: In joint work with Ein and Lazarsfeld, Karen Smith used asymptotic multiplier ideals to prove a surprising uniform containment result for valuation ideals associated with an Abhyankar valuation that is centered on a smooth point of a variety over a field of characteristic 0. A consequence of this result is that the topologies defined by the valuation ideals of two Abhyankar valuations sharing a common smooth center are comparable in a linear sense, that is, Izumi’s theorem holds for Abhyankar valuations and not just divisorial ones. Analogs of these results were proved by me in prime characteristic using asymptotic test ideals. In this talk we will highlight a mixed characteristic version of the results of Ein-Lazarsfeld-Smith using recent advances in mixed characteristic multiplier/test ideals.