Singularities mod p, and singularities in mixed characteristic

Suppose that R is a local ring of mixed characteristic. Using recent breakthrough results of André on the existence of big Cohen-Macaulay algebras, we defined a mixed characteristic analog of the multiplier ideal / test ideal and show it satisfies many of the same formal properties as its equal characteristic brethren. Using the same ideas, we show that if R is mixed characteristic and local and R/pR has F-rational or F-regular singularities, then R itself has analgous singularities in mixed characteristic. This is joint work with Linquan Ma

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