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Singularities in mixed characteristic via alterations

Karl Schwede (Utah)
Tuesday, March 5, 2024 - 1:30pm
PDL C-38
Karl Schwede

Title: Singularities in mixed characteristic via alterations
Abstract: Multiplier ideals and test ideals are ways to measure singularities in characteristic zero and p > 0 respectively.  In characteristic zero, multiplier ideals are computed by a sufficiently large blowup by comparing the canonical module of the base and the resolution.  In characteristic p > 0, test ideals were originally defined via Frobenius, but under moderate hypotheses, can be computed via a sufficiently large alteration again via canonical modules.  In mixed characteristic (for example over the p-adic integers) we show that the various mixed analogs of multiplier/test ideals can be computed via a single sufficiently large alteration, at least when one builds in a small perturbation term.  Besides unifying the three pictures, this has various applications.  This is joint work with Bhargav Bhatt, Linquan Ma, Zsolt Patakfalvi, Kevin Tucker, Joe Waldron and Jakub Witaszek.
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