Memento École Polytechnique Fédérale de Lausanne

In her thesis, Karen Smith showed that if a variety in characteristic zero had the property that its mod p reductions were F-rational for some p >> 0, then R had rational singularities in characteristic zero.

Suppose now that R is a local ring in mixed characteristic.  Suppose that R/p has F-rational singularities for some p.  We prove that R then has rational singularities in mixed characteristic and hence any localization to characteristic 0 also has rational singularities.  We also will discuss various generalizations to this statement.

This is joint work with Linquan Ma and uses recent advances in our understanding of singularities in mixed characteristic.